THE BELL SYSTEM
TECHNICAL JOURNAL
volume xliii March 1964 number 2
Copyright 1804, American Telephone and Telegraph Company
Importance of Intrasublattice Magnetic
Interactions and of Substitutional
Ion Type in the Behavior of
Substituted Yttrium Iron
Garnets
By S. GELLER, II. J. WILLIAMS, G. P. ESPINOSA
and R. C SHERWOOD
(Manuscript received November G, 1963)
The remits of measurements at moderate to high magnetic fields on a
large number of nonmagnetic ion substituted yttrium iron garnets suggest
that intrasublattice interactions play an important role in determining
their spontaneous magnetizations and Curie temperatures. It is shown that
the system { Y 3 - x Ca x \[Fe->\( Fc 3 - x Si x )O l o is continuously related to the system
\Y 3 - x Ca x }[Zr x Fe 2 - x ](Fe 3 )Oi2 or { Y 3 \[Sc x Fe 2 _ x }(Fc 3 )O n . It is concluded
that in these systems the tetrahedral-telrahedral (d-d) antiferroimujnctic
interactions are stronger than octahedral-octahedral (a-a) antiferromag-
netic interactions. The changes in magnetic structure from an ideal ferri-
magnet, yttrium iron garnet, to an end-member in which there are at least
short-range antiferromagnctic interactions (i.e., in \Ca 3 \[Fe->]( Si 3 )O l2 or a
hypothetical {YC(h\[Zr^{Fez)On) should bear an analogy to the crystal
chemical changes. It is therefore proposed that when substitution is made
exclusively in one sublattice, the moments of the Fe 3+ ions in that subfattice
remain parallel (as in the Yafet-Kittel theory), while the weakened average
a-d interactions and the intrasublattice interactions lead to random canting
of the Fe ion moments of the other. This tendency occurs as soon as sub-
stitution begins. On continued substitution, a point is reached beyond which
canting increases much more rapidly with increasing substitution. In this
region, the intrasublattice interactions dominate the a-d interactions, bid it
is probable that the canting continues to be random.
565
566 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
In the \Y 3 }[Mg x Fe 2 - x ](Fe 3 - x Si x )Oi2 system, the point at which the
tetrahedral intrasublattice interactions dominate is reached at about x =
0.95 as contrasted with x M 0.70 for the {Y 3 - x Ca x )[Zr x Fe 2 - x \{Fe 3 )On and
{Y 3 }[Sc x Fe 2 - x ](Fe 3 )Oi2 systems. The canting of the d-site ion moments
increases at the same rate in the three systems to x « 0.70, but beyond this
point, the canting in the Mg-Si substituted YIG is always substantially less
than for the other two systems. This together with data on other substituted
garnets indicates that the substitution of the Si?* ions in the d-sites tends to
decrease the average d-d interaction strength. Similarly, substitution in the
a sites tends to decrease the average a-a interaction strength.
Measurements on some garnets in the systems [ Y 3 ^uCa y } [Sc x Fe 2 ~ x ]-
{Si y Fe 3 - y )On, {Y 3 - v+x Ca y - x \[Mg x Fe2- x ](Fe 3 - y Si y )On and {Y 3 - x ^,Ca x+y }-
[Zr x Fe2- x ](SiyFe 3 -y)Ou indicate that different nonmagnetic ions may
produce different magnetic behavior. This is especially noticeable in the
region in which the intrasublattice interactions are dominant. Comparative
behavior of the systems \Y 3 )[Sc x Fe2- x ] {Fe 3 )O n and {Y 3 - x Ca x }[Zr x Fe 2 - x ]-
(Fc 3 )Oi2 and of tfie systems {Y 3 - x Ca x \[Fe2)(Fe 3 - x M x )On , M = Si and
Ge, also indicates that the ion type is important in determining magnetic
behavior. It is speculated that this remits from effects on the interaction
geometry, especially when the interactions are weak.
Results on garnets in systems \Y 3 - y Ca u )[Sc x Fe2- x ](Fc 3 - y Si y )Oi2 ,
{ Y 3 . v+x Ca y - x ] [Mg x Fe2- x ](Fe 3 - y Si y )O l 2 , and { Y 3 . x - v Ca x+v } [Zr x Fe 2 - x ]-
(Si„Fe 3 -y)Oi2 also aided in substantiating the other ideas put forward as
well as in determining the distribution of ions in the system { Y 3 \Fe h - x Al x On ,
on which more extensive studies than heretofore were made. Some anomalies
occur in this system, for values of x > 2.0.
Application of the ideas derived from these studies are made to the f err o-
spinels, and it is shown that one may thereby account for the high Curie
temperature of lithium ferrite, the lower Curie temperature of nickel ferrite,
and the substantially lower Curie temperature and low 0°K moment of
manganese ferrite.
It is noted that although the ideas presented may account in a general
way for the behavior of the Sb 5+ and V 5+ ion substituted garnets, their be-
havior could not have been quantitatively predicted from the results of the
present work. It is probable that the chemical bonding of the Sb and V
ions has much greater effects on the magnetic behavior than does that of the
various ions treated in this paper.
I. INTRODUCTION
Studies of substitutions for iron ions in yttrium iron garnet of non-
magnetic ions which prefer exclusively (or almost exclusively) octa-
BEHAVIOR OF SUBSTITUTED YIG 567
hedral sites have been reported earlier. 1 •- The results of the study of the
tin-substituted yttrium iron garnets led to Gilleo's statistical treatment, 3
which appeared to account well for the 0°K moments and Curie tem-
peratures in this system as well as in those involving zirconium, 2 scan-
dium, 2 " 1 and indium 2 " 1 substitutions. However, the data available at the
time of these developments were still not sufficient for a complete test
of the method.
The study of substituted yttrium iron garnets has now been extended
to systems in which substitution for Fe + ions is made exclusively in the
tetrahedral sites (i.e., {Y 3 _ I Ca x }[Fe 2 ](Fe 3 _. r Si. c )Oi 2 ), equally in both
octahedral and tetrahedral sites
(i.e., {Y 3 }[M gl Fe 2 _ x ](Fe 3 _ x Si x )0 12 , (Y 8 _,Ca x }[Sc x Fe2-x](Fe8-*Si*)Oi2 ,
and
{Y 8 _ 2x Ca 2l }[Zr I Fe 2 _ s ](Fe 3 _ s Si,)Oi2) J
and unequally in the two sites
(e.g., { Ys+s-yCav-x) [Mg*Fej_](Fei_J3i,)O u ,
!Y ;( _„Ca i/ }[Sc J Fe 2 _.](Fe3_„Si„)0 12 ,
and J Y;i_ J ._j / C'a J +„! [ZrJ^-J ( Fe3-»Si» ) Oi 2 ) . Analogous germanium-sub-
stituted systems have also been studied. The system { Y 3 _ x Ca x } [Zr x Fe 2 _ x ]-
(Fe 3 )()i 2 has been reinvestigated and the study of the | Y 3 j [ScrFe^]-
(Fe 3 )()i> system extended to larger values of x. High-field measurements
have been made on specimens when required. The study of the system
Y 3 AbFe s _ x Oi 2 has been extended to large values of x, and the distribu-
tion of the ions vs x deduced.
The results of these investigations indicate that the Gilleo treatment
does not in general give good agreement with the observed 0°K moments
of the substituted yttrium iron garnets. Application of the Yafet and
Kittel theory 5 to the tin-substituted garnets was made by de Gcnnes. 6
Agreement of 0°K moments appeared to be good, although not nearly
as good as that shown 23 by the Gilleo theory. However, an arithmetic
error was made in de Gennes' calculation; when corrected, the agree-
ment deteriorates. Furthermore, using the same approach as that of de
Gennes for the silicon-substituted garnets, that is, assuming the Pauthe-
net 7 molecular field coefficients of yttrium iron garnet to remain con-
stant for the whole system, no semblance of agreement is found.
Contrary to earlier assumptions, there is substantial evidence that
m/rasublattice interactions are not negligible; they appear to play an
important role in determining the spontaneous magnetizations and Curie
568 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
temperatures of the substituted garnets. It also must be concluded that
different nonmagnetic ions may produce different effects on the mag-
netic behavior when the amounts of substituent for the Fe 3 * ions in
particular sites are the same.
In the course of our study of the yttrium iron garnet-calcium iron
silicate system, on which a preliminary report was made some time ago, 8
we learned that Smolenskii, Polyakov, and Iodin 9 had reported on this
system. However, their magnetic measurements were made at 77 °K and
presumably they did not make any high-field measurements.
The above description should make it clear that the problem of the
behavior of the substituted garnets has increased in complexity with
the number of experiments performed. Following the completion of the
draft form of this manuscript, new garnets containing Sb 6 " 1 " (Ref. 10),
V 6 * (Refs. 10-12), and Bi 3+ (Refs. 10, 12, 13) ions were discovered.
(Many of these no longer contain yttrium or rare earth ions.) The
magnetic behavior of these garnets was in part unpredictable from the
results given in the present paper. However, there are unifying con-
sistent features of the garnet systems described herein and we feel it
worthwhile to describe them.
Complete understanding, it is felt, will eventually come from various
studies of single crystals in the various systems. Neutron diffraction
studies should play an important role, but also of utmost importance,
it would appear, are spectroscopic studies which would give an insight
into the effects of changes in chemical bonding on changes in magnetic
interactions.
II. EXPERIMENTAL
2.1 Preparation of Specimens
As we have recently described in some detail our present techniques
for specimen preparation, 14 we shall not do so here. Utmost care is
required in these preparations, including the use of pure starting ma-
terials, correction for adsorbed moisture or C0 2 in the starting materials,
proper mixing and avoidance of inhomogeneous loss of constituents,
the insuring of the theoretical weight losses on firing, the careful exami-
nation of powder photographs or diff ractometer patterns to be sure that
single phases, preferably sharply defined ones, are obtained, and careful
measurement of lattice constants to be sure that these fit properly on
the curves characterizing the systems. The preparation of the specimens
in most cases required several regrindings and refirings.
BEHAVIOR OF SUBSTITUTED YIG 569
2.2 Magnetic Measurements
Measurements of magnetic moment were made in the temperature
range 1.4-298°K at applied fields, //„ , to 15.3 koe, by means of a pen-
dulum magnetometer described elsewhere. 15 Calibration was carried out
with spectroscopically pure Ni; measurements ou Mohr's salt 10 corrob-
orated the calibration with Ni.
Measurements at fields to 80 koe were made with the Bitter-type
magnet and an extraction method used for determination of the moment.
Calibration was carried out with spectroscopically pure Ni.
2.3 Crystal I ographic Measurements
Lattice constants were obtained from measurements of powder
photographs taken with Norelco Straumanis-type cameras of 114.6-mm
diameter and CrK radiation.
III. MAGNETIC AND CRYSTALLOGRAI'HIC DATA
3.1 The Systems \y 3 _ s Ca x \Fe 5 _ r M s 4+ O n , M = Si, Ge
.3.1.1 Magnetic Data,
In the system | Y: t _ T Cii J .)Fe5_. r Si. f Oi2 , specimens with .t ^ 1.77 were
saturated at fields ^ 1 2.6 koe at 1.4°K. For x ^ 1.88, saturation was
not attained at low fields, and therefore measurements were made at
the high fields at 4.2°K. The specimen with x = 1.88 was saturated at
GO koe. None of the other specimens was saturated at fields below 80
koe and at 4.2°K. For these specimens the behavior of the magnetiza-
tion at fields ^50 koe was such that /(«(//„ ,7') = n B (0,T) +
Xndfa ,T)H„ ; the values of n B (0,T) in these cases were determined by
extrapolation to H a = 0.
Typical curves of n h (H a ,T) va T obtained with the pendulum mag-
netometer are shown in Figs. 1 and 2. When x = 2.25 (Fig. 2), the
magnetization curves at the two higher fields appear to reach a maxi-
mum at about 40°K, then decrease, cutting the ordinate with positive
slope. At 5 koe, the curve cuts the ordinate with zero slope. The curves
for x = 2.50 behave similarly.
In Fig. 3, curves of n B vs //„ at 4.2°K for x = 2.00, 2.25, and 2.50 are
shown. For all these, measurements were made on sintered specimens.
For x = 2.25, measurements were also made on the finely powdered
specimen. Note that although the slope is greater for the sintered speci-
570
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
{Y,.23Ca,. 77 }[Fe 2 ]CFe 1 . 23 SL,. 77 )0 12
5 kofH
Ji4.24k0e
SO 100 150 200 250
TEMPERATURE IN DEGREES KELVIN
Fig. 1 — n a vs T at different magnetic fields for
(Y 1 .2 3 Cai. 77 |[Fe s ](Fei.23Sii.77)Oi2.
men, extrapolation to H a = leads to insignificant difference in n B .
However, when a plot of n B vs \/H a is extrapolated to l/H a = 0, these
values of n B are 3.5 and 4.0 for the powdered and sintered specimens
respectively.
In Table I, the spontaneous moments listed for specimens with
x ^ 1.77 are extrapolated to 0°K; for specimens with x ^ 1.88, the
values are those extrapolated to H a = at 4.2°K. 17 These are plotted
vs x in Fig. 4. Negative values of n„ mean that the moment of the octa-
hedral sublattice is dominant.
Where possible, Curie temperatures (Table I and Fig. 5) were ob-
tained from extrapolation of a plot of n B (0,T) vs T to n B \0,T) =
n R 1
k£
r^v {Yo.75Ca 2 . 25 }[Fe 2 ](Fe . 75 SL 2 . 25 )0 12
*\\^,^14.24 kOe
^\. \1\ ,^9.6 »
50 100 150 200 250
TEMPERATURE IN DEGREES KELVIN
Fig. 2 — n B vs T at different magnetic fields for
|Yo.7 B Ca2.25llFe2](Feo.7=Si 2 .2B)0, 2 .
BEHAVIOR OK SUBSTITUTED YIG
571
{VxCa I }[Fe 2 ](Fe 3 _ x SL B )0 1 .
30 40 50
H a ,kOe
Fig. 3 — n B vs applied field, //„ , at 4.2°K, for some specimens in the system
|Y 3 -xCa,|[Fe-.](Fe 3 _ I Si I )0 1I .
and from extrapolation of l/x„ vs T to \/%„ = when T c was suffi-
ciently below room temperature. (See Ref. 14.)
The garnet [Ca^f l' ?c 2](Si 3 )0|., cannot be made by solid-state reaction
at atmospheric pressure. Small crystals were grown by Van Uitert and
Bonner, and magnetic measurements were made on 2.99 g of these over
Table 1 — Magnetic and Crystallographic Data for the Garnets
J Ya-iCax) Fes. ,M/+0 12 , M = Si,Ge
M =
= Si
M =
iGe
5.01
Tc(.'K)
553 b
■i(A)
a /i"
T C {°K)
o(A)
((.()()
12.376 ±
0.003
5.01
553 b
12.376 ± 0.003
0.40
2.08
543 '
12.34 1
0.70
12.375
0.75
50S"
12.314
1.00
0.06
12.291
0.18
12.372
1.01
-0.07
12.201
1.02
-0.14
12.291
1.50
-2.36
367
12.243
-2.31
365
12.365
1.75
-3.15
316
12.360
1.77
-3.40
312
12.212
1.88
-3.8
280
12.202
2.00
-3.8
266
12.186 ±
0.005
-3.15
258
12.355
2.25
-1.9
180
12.157
-1.55
180
12.348 ± 0.004
2.50
-0.65
86
12.126
-0.35
80 (?)
12.339
2.75
12.093 d
12.329
3.00
12.048* ±
0.003
f
12.320b
R For M ■ Si, Ge and x < 1.88, 1.75 respectively, values are those from ex-
trapolation to 0°K; for x ^ 1 .88, 1.75 respectively, values are at 4.2°K, extrapo-
lated to H„ = 0. '' From J. Loriers and G. Villers, Compt. Rend., 252, 1590 (1961).
c Measured by E. A. Nesbi It. d Not single-phase : see text. " From Ref . 20. 'From
Ref. 21. "From Ref. 38.
572 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
^B
Fig. 4 — Spontaneous magnetizations vs composition for the silicon- and ger-
manium-substituted yttrium iron garnets. For x < 1.88, saturation was attained
at low fields and n B values obtained by extrapolating n B (T) to T = 0°K. For a; ^
1 88, saturation was not attained at low fields, and the n B values were obtained
by extrapolating n B (H a ) toH a = at 4.2°K (see Fig. 3). Shown also are the curves
given by the Gilleo and Neel models for substitution by nonmagnetic ions ex-
clusively on tetrahedral sites.
the temperature range 1.4 to 296°K. At a field of 5.0 koe, there was a
peak in the susceptibility at about 9°K. However, the nature of the
peak is not conclusive evidence of an antiferromagnetic transition. On
the other hand, d p for the specimen is 29°K, which is indicative of anti-
ferromagnetic interaction. The Curie constant C = AT '/A (1/xn) =
1.47 X 10~ 3 , to be compared with the theoretical value of 1.56 X 10 .
BEHAVIOR OF SUBSTITUTED YIG
573
600
p 500
w 400
300
i 200
vh ^^^
l. {Yal^gxFez-
2.{Y 3 }[s Ca: Fe 2 - a
e] (Fe 3 - X
](Fe 3 )0
SL x )0 l2
12
\\
3. {Y 3 _ a: ca x }[Fe 2 J(Fe3_iSLx)0 12
\\ OBSERVED
X\ GILLEO MODEL
V
\
\
0.5
1.5
X
3.0
Fig. 5 — Curie temperatures vs x for the systems (1) {Y 3 J[MgxFe2-il-
(F e3 -xSi x )0 12 , (2) {Y 3 )[Sc I Fe 2 _ I ](Fe3)0 1 , , (3) {Ys-xCa.j [Fe 2 ](Fe 3 _ x Si I )0 12 .
In the system JY3_. r ('a. r |Fe5-iGe I Oi2 , specimens with x S 1.50 were
saturated at fields ^ 12.fi koe at 1.4°K. In measurements with the
pendulum magnetometer, the specimen with x = 1 .75 appeared to be
saturated at 9.6 koe at both 1.4 and 4.2°K. Measurements on the sin-
tered specimen at high fields at 4.2°K indicated that saturation was not
attained until about 50 koe. However, the difference in n B is only 0.1 y. B .
For the specimens with x ^ 2.00, saturation was not attained at 1.4° or
at 4.2°K at fields below 80 koe. As in the case of the first system dis-
cussed, n B (0, 4.2°K) was determined by extrapolation of the straight
line portion of the n B (H a ,4.2°K) vs H a curve to H a = 0. The mag-
netization curves in this system were similar in character to those of
the specimens in the analogous Si system. Curie temperatures (Table I)
were determined as described above. The spontaneous magnetizations
extrapolated to T = 0, //„ = or at T = 4.2°K, 17 H a = are listed in
Table I and plotted vs .r in Fig. 4.
3.1.2 Crystallographic Data
The lattice constants of specimens in these systems are listed in Table
I and plotted vs x in Fig. fi. All garnets involving Ge substitution gave
574 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
12.2
12.0
Fig. (5 — Lattice constants vs composition of silicon- and germanium-substi-
tuted garnets.
final powder photographs having sharp back-reflection lines. However,
in a few cases of the silicon-rich specimens (that is, with X = 2.25 and
2.50) sharp back-reflection lines appeared to be unattainable. Because
no extraneous phases appeared to be present, it seemed worthwhile to
carry out the magnetic measurements on these anyway. In some cases,
the indicated larger limits of error on the lattice constants are a result
of only few back-reflection lines on which the measurements are based.
However, because of the smoothness of the curves which may be passed
through the central values, all the indicated estimates of limits of error
(Table I) are felt to be conservative.
In both systems, the lattice constant vs composition behavior is
nonlinear; such behavior has been observed in other garnet sys-
tems. 114 ' 1819 We might expect the larger volumes than given by the
straight line joining the lattice constants of the end-members to indi-
cate greater entropies, the disorder apparently arising from the dis-
BEHAVIOR OF SUBSTITUTED YIG 575
parity of the sizes and possibly of the electrostatic charges of tetrahe-
drally coordinated ions of Fe 3+ vs Si 4+ or vs Ge 4+ . However, the lattice
constant itself is not always indicative of the disorder which may exist
in a solid solution. The latter cannot obey the third law of thermo-
dynamics because the crystalline fields about space group equipoints
cannot all be the same, even if the lattice constant-composition behavior
is a linear one.
An attempt was made to prepare the specimen with M = Si, x =
2.75; a slight amount of an extra unidentified phase was observed in
this case. The lattice constant (Table I) indicated that the garnet
phase present had almost the composition sought. However, it is pos-
sible that some excess silicon with divalent iron could be present in this
garnet. 14
The specimen of Ca 3 Fe 2 Si 3 0i2 prepared by Van Uitert and Bonner
had a lattice constant of 12.067 =fc 0.003 A. This is substantially larger
than the 12.048 A reported 2 " for a specimen prepared at high pressure.
The difference in lattice constant implies that at least one of the speci-
mens contains impurity ions. However, our main interest was to show
the presence of antiferromagnetic interaction in CasFesSisOi-j , and it
does not seem that the impurity ion (or ions) could introduce it in this
case. Magnetic measurements were also made on a mineral specimen
from Graham County, Arizona, having a lattice constant of 12.008 ±
0.003 A, with essentially the same results as obtained on the synthetic.
.•{.1.3 Discussion of the Garnets \Y- i C'a\[['\--<\(Fe-.Si)0 V i and
[Y£a}Fe,GeOn
The present work indicates that earlier results 21 on these garnets are
erroneous. The 0°K moments reported earlier were 0.5 and 1.5 n„
respectively, as compared with 0.00 and 0.18 /x« obtained in the present
work. That the latter two results are the more reliable is easily ascer-
tained by examination of Fig. 4; these points lie well on the curves for
the appropriate systems.
It is precisely in sensitive regions where the greatest care in prepara-
tion must be exercised. In the case of the Si-substituted garnet, we can
only guess that perhaps there was present in the earlier preparation an
extraneous phase which was not observed on the powder photograph or,
that despite the good agreement between lattice constants (see Tables
I of Ref. 21 and of this paper), the stoichiometry was not exact. For
example, excess Si 4+ ions would cause the reduction of some Fe 3+ to
Fe ions. While the excess Si 4+ ions would tend to reduce the lattice
570
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
constant, the presence of Fe 2+ would tend to increase it. Also, any
deviation in stoichiometry would tend to increase the absolute value
of the spontaneous moment.
In fact, the observed deviation, 0.06 m« from exactly 0.00 mb for
{Y 2 Ca}[Fe 2 ](Fe2Si)Ou, amounts to only 0.5 mg of Si0 2 in the 0.001
mole of specimen prepared. The specimens with x = 1.01 and 1.02 were
also prepared in an attempt to find the exact zero spontaneous mag-
netization at 0°K for this system. However (see Table I), neither of
these gave exactly zero values. It would appear from the results that
the experimental error could be as large as the equivalent of 0.01 of a
Si 4+ ion or 0.05 p B in this region of the system.
The high value previously obtained for the garnet {Y 2 Ca}Fe4GeOia is
more easily explained, and a number of experiments (see Table II)
were carried out to prove this contention. Examination of Fig. 6 shows
that the change of lattice constant with x in the system
{Y 3 -iCa I }Fe B -xGe I Oi2 is not very o large over rather large ranges of x.
At x = 1.00, a change of ±0.003 A (our quoted limits of error) implies a
change of -0.25 or +0.20 respectively in x, which in turn implies a
change (Fig. 4) of ±1.00 m« in 0°K moment. The broadness of back-
reflection lines in the x-ray powder photograph may indicate a variation
in range greater than 0.75 ^ x £ 1 .20. As shown in Table II, repro-
Table II — Experiments to Obtain the Correct Data for
(Y,Ca}Fe 4 GeOi2
Specimen
a(A)
«B
(1.4°K)
(77°K)
Description
594
12.372
1.00
After firing 16 hrs. at 1300°C, then 16 hrs. at
1350°C. Specimen contained 6.5% excess
GeOj (based on total Ge0 2 ). Broad 116 a
line.
12.371
0.23
After third firing 39 hrs. at 1425 °C. Speci-
men contained 4.1% excess GeOj . Sharp
116 line.
602
12.371
0.18
0.17
After firing 19 hrs. at 1405°C, then 63 hrs. at
1400°C. Sharp 116 line.
12.372
0.17
After third firing 66 hrs. at 1300°C. Sharp
116 line.
(.00
1.12
1.08
0.90
0.28
After firing 10 hrs. at 1315°C, then 16 hrs. at
1300°C. Broad 116 line.
After third firing 64 hrs. at 1275°C. 116 line
still broad.
After fourth firing 17 his. at 1410°C. 116 line
much sharper.
12.372
0.18
After fifth firing 16 hrs. at 1410°C. 116 line
sharp.
That is, h* + A: 2 + I 2 = 116.
BEHAVIOR OF SUBSTITUTED YIG 577
ducible results are obtained for single sharply defined stoichiometric
phases.
The preparation of { Y 2 0aj Fei(ie()i 2 requires a temperature of about
1400°C; even rather long firings at about 1300°C did not produce
homogeneity. On the other hand (see Table II, specimen 002), firing at
1300°C for a long period produced no significant change in a homogene-
ous specimen formed at 1400°C
Because of its volatility, an excess of Cie0 2 is usually added to the
reactants required for the preparation of Ge 4+ ion substituted garnets.
Firings are carried out until this excess is lost. It is possible, however, to
add too great an excess and it is then best to discard the specimen.
However, as seen in Table II, for specimen 594, an excess of 4.1 per cent
Ge0 2 was not as important as the correct firing temperature.
3.2 The System* \ Y 3 ) [Sc x Fe 2 -,](Fe 3 )0 12 and \ Y^ x Ca x \ \Zr x Fe^ T }-
(Fc,)O n
:i.2.i Magnetic Data
Part of the {Y 3 }[Sc x Fe 2 _,](Fe 3 )Oi 2 system 4 and the whole {W.Ca,}-
[ZivFcM-j-lf Fc s )Oi 2 system" have been investigated earlier in these labora-
tories. In the present investigation several new specimens have been
prepared and high-field measurements made on specimens with x ^ 0.72.
For values of x ^ 0.00, specimens were magnetically saturated at an
applied field of 9.0 koe at 1.4°K. For x = 0.72, the specimens were
saturated at 00-70 koe at 4.2°K, and for x > 0.72, saturation was not
attained at fields to 80 koe at 4.2°K. In these cases the spontaneous
magnetizations, w fl ( 0,4.2°), were obtained by extrapolating the straight
line portions of the n n (H a ,4.2°) to //„ = 0. The values thus obtained
are listed in Table III; the actual spontaneous magnetizations of 0°K
may, of course, be slightly higher. Spontaneous magnetizations ob-
tained by extrapolating n B (H a ,4.2°) vs 1/H a to l/H„ = are also
shown in Table III. The spontaneous magnetizations are plotted vs x
in Fig. 7. Curie temperatures (Table III, Fig. 5) of specimens in these
systems were determined as described above. For x ^ 1.50, results were
inconclusive. Examples of plots of n H vs T for specimens in these systems
have been given in other papers. The behavior of n B vs T for high sub-
stitution is similar to that of the ! Y ;,_.,( 'a x |[Fe 2 ]( Fen-j-Si^Opj system for
high .r.
The values ««(//„ ,4.2°) vs //„ for high x of specimens in both sys-
578
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
Table III — Magnetic and Crystallographic Data for Garnets
{ Y 3 } [Sc*Fe2_J(Fe 8 )Oi2 and { Y 3 -xCa*} [Zr x Fe 2 _ x ](Fe 3 )Oi 2
Sc
Zr
X
»B a
«»"
a(A)
T C (°K)
o<A)
r c (°K)
//„ =
H a =
H a =
Ha -
0.20 b
5.9
5.9
12.404
0.25 c
5.99
5.99
504
12.392
0.40 1 '
6.7
6.7
12.434
0.60
7.44
7.44
408
12.424
7.39
7.39
12.470
0.72
7.65
7.65
386
12.433
7.6
7.6
386
12.490
0.75 p
375
12.438
0.80
7.1
8.1
12.442
6.9
8.2
12.501
1.00
5.7
7.6
294
12.457
5.2
6.6
288
12.534
1.25
3.1
6.2
200
12.478
2.8
5.7
200
12.573
1.50
1.4
4.6
100(?)
12.497
1.1
4.0
65(?)
12.614
1.75
0.4
2.0
48(?)
12.653
1.95
0.0
12.684
» For x < 0.72, n B was obtained by extrapolation to T = 0; for x ^ 0.72, n B
is at 4.2°K. b Data from Ref. 2. c Data from Ref. 4.
terns are plotted in Fig. 8. In all cases, for the same value of x, the
values of n„ at the same II a are higher for Sc substitution than for Zr
substitution. This will be discussed further later.
A plot of 1/xn vs T for {Yi.osCa.^KZr^Feo.osKFejOOiz is given in
Fig. 9. A conclusive anti ferromagnetic transition was not observed at
fields as low as 4.9 koe. Above 70°K, 1/x* follows a Curie- Weiss law
with C equal to the calculated theoretical value for 3.05 Fe 3+ ions per
formula unit. The linear portion of l/x» vs T intersects the abscissa at
— 66°K, indicating that there is antiferromagnetic interaction among
the Fe 3+ ions at low temperatures.
Shown also in Fig. 9 is a plot of l/x„ vs T for (YCa 2 }[Zr 2 ]-
(Gao. 2 6Fe 2 .7 5 )0]2 . In this case again, there was no conclusive evidence
of a transition to long-range antiferromagnetic order, but the inter-
section of the extrapolated linear portion of l/x» vs T with the abscissa,
— 40°K, indicates that antiferromagnetic interaction is present at low
temperatures. As one would expect, the interaction strength is weaker
than for { Yi .osCai .95) [Zn . 96 Fe .os] ( Fe 3 ) Oi 2 .
For both specimens, there does not appear to be any indication of
weak ferromagnetism. 22 Below the linear portions of 1/xn vs T, the
curves are concave upwards and neither specimen appears to have a
residual moment at 1.4°K.
BEHAVIOR OF SUBSTITUTED YIG
570
2.0
Fig. 7 — Spontaneous magnetizations vs composition for the zirconium- and
scandium-substituted yttrium iron garnets. For x < 0.72, saturation was attained
at low fields and the n« values were obtained by extrapolating ««('/') to T = 0°K.
For j ^ 0.72, saturation was not attained at low fields and the n B values were
obtained by extrapolating ««(//„) to//„ = at 4.2°K (see Fig. 8). Shown also are
the curves given by the (Jilleo and Nt'el models for substitution by nonmagnetic
ions exclusively on octahedral sites.
3.2.2 CrystaUographic Data
Lattice constants for these systems are given in Table III and plotted
vs x in Fig. 10. Shown also in Fig. 10 are values obtained in the former
studies made in these laboratories. For the most part, agreement of the
former with the present values is good. However, in the present study,
580
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 19G4
{Y 3 }[sc B Fe 2 ^](Fe 3 )o„
8 UY 3 -j,jCa,B} [zr a ,Fe 2 - ;E ](Fe 3 )O l2
5C
Fig. 8 — tin vs .applied field H a , at 4.2°K, for some scandium- and zirconium-
substituted yttrium iron garnets.
X n
■do
* {Y,.o 5 Ca 1 . 95 }[zr 1 . 95 Fe 00 J (Fe 3 )0, 2
S*
16
o {vca 2 } [zr 2 ] (Ga . 25 Fe 2 .75) 12
^^s
V^ N THEOR.
^.Y (FREE")
^* * MONS/
^
*$J05 Fe 3+ IONS
<?
^S^S 1 ^^^ 1
-50
50 100 150 200 250 300
TEMPERATURE IN DEGREES KELVIN
Fig. 9 — Reciprocal susceptibility (x« in Bohr magnetons per oersted per
formula unit) vs temperature for the garnets {Yi. 6Cai. 9 i>)[Zri.96Feo.o5](Fe3)Oi2
and |YCa 2 }[Zr2](Gno.2sFeo. 7 ii)Oi2 .
BEHAVIOR OF .SUBSTITUTED YIG
581
all points for both systems lie almost exactly on the two straight lines
(Fig. 10) and, where differences occur, the present values are considered
to be the more reliable ones.
An attempt to prepare {Y 3 |[Sc 2 ](Fe3)Oi 2 produced a specimen con-
taining an extraneous perovskite-type phase and a garnet phase with
lattice constant 12.508 A. This value corresponds to the composition
x = 1.62, which is the maximum value attainable, at least under the
conditions of preparation.
12.64
12.60
12.52
12.36
{
y 3 -x Ca x}[ Zr x F e 2 . x ](Fe 3 )0 12 I
o PRESENT WORK /
A FROM REFERENCE 2/
y
f
/k
A VMY 3 }[sc I Fe 2 . ;r ](Fe3J
/ / o PRESENT WORK
d / A FROM REFERENCE
4
f 4
0.8 1.2
X
Fig. 10 — Lattice constants vs composition for the scandium- and zirconium-
substituted yttrium iron garnets.
582 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
In the case of Zr substitution, previously we reported obtaining a
specimen with x = 2.00. However in attempting to reproduce this com-
position, veiy careful examination of x-ray data indicated a slight
amount of extraneous phase. The garnet present had a lattice constant
12.086 A, indicating a maximum x = 1.90. It was possible, however, to
make the garnet {YCa 2 }[Zr2](Ga .26Fe2.76)Oi2 2a with lattice constant
12.681 ± 0.003 A.
3.3 The System Y 3 [MgJ'e^iFe^SQOu
3.3.1 Magnetic Data
For values of x ^ 0.85, all specimens in this system were essentially
saturated over the whole temperature range at fields of 9.6-12.6 koe.
For x = 0.90, measurements were made only at 1.4°K; the specimen
was saturated at 11.3 koe. For x = 1.00, saturation was attained at 11.3
koe at 1.4°K, yielding a spontaneous magnetization of 3.5 n„ per formula
unit. However, subsequent high-field measurements showed that this
specimen was more likely saturated at 70 koe with a moment of 3.8 n n .
For x ^ 1.10, saturation was not attained at 1.4°K and at fields
^14.24 koe; therefore high-field measurements were made on these
specimens at 4.2°K. The specimen with x = 1.10 was saturated at 70
koe. All others were not saturated below 80 koe; in these cases the values
of spontaneous magnetization were obtained by extrapolation of the
lineal- portions of the n B vs H a curves to //„ = 0. Values of moments
were also obtained by extrapolation of n„ vs l///„ to l/// a = 0. Both
sets of values are given in Table IV and plotted vs x in Fig. 1 1 . Note
that the points for x = 1.00 and 1.10, which must lie on a reasonable
curve representing the system, fit distinctly better on the n B (0) than
on the n B ( °° ) curve.
Curves of n B vs T at 14.24 koe for various specimens are given in
Fig. 12. To show the effect of different fields on the magnetization when
saturation is not attained, typical curves for the specimen with x = 1 .25
are given in Fig. 13.
When x = 1.7, there appears to be an antiferromagnetic transition
at about 10°K. This is seen at fields of 9.6 koe or lower. There appears
also to be a residual moment of £^0.2 n B at 4.2°K.
Measurements were made on the specimen with x = 0.55 at fields
from 4.8 to 80 koe at 4.2°K. Saturation was attained at 4.8 koe; the
moment obtained was 4.62 n B , an excellent corroboration of the value
obtained with the pendulum magnetometer (Fig. 12).
Curie temperatures, obtained from plots of n B 2 (0,T) vs T (see above)
BEHAVIOR OF SUBSTITUTED YIG
583
Table IV — Crystallographic, Magnetic and Preparation Data
for {Y 8 }[Mg i Fe2-,](Fe 3 - I Si I )Oi2 System
X
a (A)
"B a
r c (°K)
Firing Procedure, Temp., °C (hr)
0.40
12.348
4.05
432
1250(2), 1425(24), 1445(24)
0.55
12.330
4.00
396
1 400 (4), 1450 (24), 1405 (24)
0.70
12.321
4.35
350
1450(4), 1480(3), 1500(3)
0.85
12.308
4.25
327
1400(4 ), 1490(2), 1500(2), 1550(2)
0.90
12.305
4.17
1400(4), 1400(2), 1540(2)
1.00
12.280
3.8(3.8)''
205
1420(f), 1480(3), 1520(3), 1500(2)
1.10
12.282
3.2(3.2)
220
1420(1), 1480-1500 (44), 1520 (4)
1.25
12.205
2.2(3.4)
187
1450(4), 1525(3), 1550(3)
1.40
12.252
1.25(2.7)
110
1400(4), 1500(2), 1500(2)
1.50
12.237
0.9(2.4)
84
1400(4), 1500(4), 1525(5), 1550(5)
1.(50
12.229
0.55(2.0)
50(?)
1400(4), 1500(34), 1525(2), 1500(2)
1.70
12.220
0.35(2.25)
1375(1), 1500(2), 1550(4), 1590(4), 1575(4)
1.85
12.197
1300(1), 1£00(4), 1525(4), 1535 (7)
1 For x ^ 0.90, n u was obtained by extrapolation to T = 0; for x > 0.90,
iin i.s at 4.2°K. '• All specimens were first calcined at 500-900°C over a period of 1
hr. ° Numbers in parentheses are from extrapolat ion to H a = °° , others to H a = 0.
and 1/xn vs T when possible, are listed in Table IV and plotted vs x in
Fig. ">. The Curie temperatures obtained from the Gilleo treatment agree
almost perfectly with those observed. The discrepancies are noticeable
only at high x: for x = 1.5, it is 9°K, for x = 1.6 it is 14°K.
3.3.2 Crystallographic Data
Lattice constants for this system are given in Table IV and plotted vs
x in Fig. 14. The limits of error assigned to each lattice constant are
±0.003 A. All points but one deviate no more than 0.002 A from the
curve a vs x, and in no case is more than a deviation of x = 0.02 implied
by any deviation of lattice constant; in fact, a deviation of x = 0.02 is
implied for only three out of thirteen specimens, namely for those with
x = 0.00, 1.00 and 1.70.
Careful examination of the powder data, both photographic and
diffractometric, indicated that specimens with x = 1.90, 1.95 and 2.00
were not single-phase. As it is known that the Mg + ion may also occupy
c sites in garnets, at least one specimen was made in which substitution
was made in both c and a sites simultaneously. The garnet {Y2.8Mgo.2i-
[Mgi. 7 Fei. 3 ](Fei.iSii.9)Ou has a lattice constant of 12.177 ± 0.00.3 A.
Because such substitution is feasible, the exact maximum value of x
in the { Y3)[Mg J .Fe2-x](Fe 3 - J -Si J )Oi 2 system cannot really be obtained
and the preparation of specimens in this system requires more care
perhaps than those in which a substituent ion prefers one site exclusively.
(For this reason, we have included the firing data in Table IV.)
584 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
n B 2
Fie 11 — Spontaneous magnetizations vs composition for the system |Y 3} -
[Mg«Fej_«J(Fe3_xSi«)0is . For x ^ 0.90, saturation was attained at low fields and
the n B values were obtained by extrapolating n H (T) to T = 0°K. For 3- ^ 1 .00,
saturation was not attained at low fields and the n B values were obtained at 4.2 K
by extrapolating n«(f/„) to H a = and n*(l/ff.) to \/H„ = 0. Shown also is the
curve given by the (iilleo model.
50 100 150 200 250
TEMPERATURE IN DEGREES KELVIN
300
Fig 12 — n«(14.24 koe.T) vs T for specimens in the system
|Y,}[Mg,Fe*-*](Fei-,Si,)0 1 j.
BEHAVIOR OF SUBSTITUTED YIG
585
2.4
n B
{Y 3 ][Mg 1 . 25 Feo.75](Fe,.75SL l .25)o l2
O 40 80 120 160 200 240
TEMPERATURE IN DEGREES KELVIN
Fig. 13 - iiu va T :it different magnetic fields for
|Yi)[Mgi.s S Feo.7i](Fei.7iSii. 88 )OiJ.
The behavior of the lattice constant vs composition (Fig. 14) is
again not linear for the [ Y : ,)[Mg r l''e 2 _ x ](Fe3_ J .Si J )Oi2 system. However,
;is will he shown later, of all the ions substituted for trivalent iron, the
Mg 2+ ion appears to make the "best fit," in the octahedral sites.
3.4 Miscellaneous Specimens in the Systems \ Y-i- y Ca u \ [Sc x Fe2-*\-
(Si y Fe 3 - u )O l2 , j Y 3 . y+x Cay^\[Mg x Fe^](Si u Fe^)O n and
{ Y^-yCas+y) [Zr x Fe^. x ](SiyFe*- v )On
Measurements were made on various specimens in these systems for
the purpose of making certain points to be given later. In some cases,
magnetic saturation was attained at low fields, in some at high fields,
and not in some at fields to 80 koc. Results are given in Table V. Several
Ge-substituted garnets analogous to the Si-substituted ones were also
made. Data for these are given in Table VI.
3.5 The System YzAl x Fes-JDn
3.5.1 Magnetic Data
Results obtained in these laboratories on part of this system were
reported several years ago. 4 In the present investigation, the range of
586 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
12.38
12.34
12.30
°<
3 12.28
(0
12.22
12.18
{Y 3 } [Mg x Fe 2 _a.](Fe3_ B SLa.)O i2
i
\
\
0.5
1.0
X
2.0
Fig. 14 — Lattice constaiit vs composition for the system
IVallMgxFe^xKFea-xSyOis .
substitution has been extended. In this system, for x ^ 1.75, magnetic
saturation was attained at 1.4°K at applied fields ^9.6 koe.
Although there is no doubt that the specimen with x = 2.0 has a
spontaneous magnetization, the results on the two specimens with x =
2.5 and 3.0 are not conclusive. In both cases, there appears to be an
antiferromagnctic transition at about 10°K (see Fig. 15) which appears
at fields of 4.8 and 9.0 koe, but not at 14.24 koe. The plots of l/x» vs
T follow a Curie- Weiss law. For x = 2.5, the straight line portion of
l/x„ vs T intersects the T axis at -40°K and for x = 3.0 at -20°K.
(See Fig. 16.) The values of Meff are 3.29 and 3.34 m« respectively. These
results indicate that at least short-range antiferromagnetic interaction
is present over a wide temperature range.
High-field measurements at 4.2°K were made on specimens with x =
2.0, 2.5, and 3.0. Each showed a residual moment when n B {H a ) was
extrapolated to H a = 0. The values obtained lie on the smooth curve
joining the points at values of x < 2.0. This, however, may be fortuitous.
BEHAVIOR OF SUBSTITUTED YIG
587
Table V — Magnetic and Crystallographic Data for Garnets
{ Y^+.Ca^j [Mg.Fea-JCSiyFe^Oia , { Ya-yCa*} [Sc x Fe2-x]-
(Si tf Fe 8 _„)Oi2 and j Y 3 _ x _„Ca J+J/ ) [Zr x Fe 2 - x ](S\yFei-y)Oi2
Appro*.
Ion
X
y
"«"
T C , (°K)
Saturation
Field, koe
a(A)
Mg 2+
0.175
0.825
1.G4
450
4.8
12.309
0.30
1.47
-0.92
4.8
12.246
0.18
1.57
-1.83
7.3
12.237
0.90
1.10
3.2
294
9.6
12.283
0.50
1.50
-0.24
325
9.6
12.244
0.44
1.76
-1.29
298
9.6
12.223
0.22
1.98
-3.1
245
60
12.191
0.75
1.75
-0.18
250
11.3
12.214
tfc 3+
0.85
0.85
4.0
12.0
12.381
0.30
1.47
-0.92
4.8
12.270
0.30
1.52
-1.12
<4.8
12.265
0.30
1.60
-1.39
<4.8
12.258
1.10
0.90
2.8
220
>70
12.398
1.00
1.00
2.9
235
>70
12.380
0.90
1.10
2.8
260
>70
12.362
Zr*+
0.70
0.21
5.9
340
>70
12.475
0.00
0.00
4.39
300
9.0
12.421
0.35
1.15
0.88
370
4.8
12.331
0.30
1.20
0.41
9.0
12.319
0.85
0.85
3.6
70
12.440
0.30
1.60
-1.40
4.8
12.277
1.10
0.90
1.8
190
>70
12.477
1.00
1.00
2.1
200
>70
12.450
0.90
1.10
1.9
210
>70
12.420
0.00
1.00
-0.3
200
12.32
1.25
1.25
12.400
■ When approximate saturation field is ^00 koe, these values are at 4.2°K;
when >70, they are extrapolated to //„ = 0. All others at or 1.4°K.
Table VI — Magnetic and Crystallographic Data for Garnets
| Ya-^+XX-x } Mg^es-jr-uGeyOu , \ Y 3 - ;/ Ca„} 8c x Fc b - x - u Ge u Oi2
and { Ya-^/'a^,,} Zi-xFes-x-j/GeyOia
Octahedral
Ion
X
y
»«*
r t '(°K)
Saturation
Field, koe
«(A)
Mg 2 +
1.00
1.00
3.9
00
12.364
1.25
1.25
2.2
>70
12.362
Sc 3+
1.00
1.00
2.9
>70
12.457
ZH+
0.00
0.00
4.35
360
9.0
12.407
0.85
0.85
2.9
>70
12.500
1.00
1.00
1.6
>70
12.530
See footnote, Table V.
588 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
0.3
0.2
20 40 60 BO
TEMPERATURE IN DEGREES KELVIN
Fig. 15 — n B vb T at different magnetic fields for Y 3 Al 3 Fe20i 2 .
The values of n B at H a = 0, T = are listed in Table VII and plotted
vs x in Fig. 17. The value for the specimen with x = 1.00 fits the curve
somewhat better than that obtained in the previous work. 4 Curie tem-
peratures, obtained as described earlier, are given in Table VII and
plotted vs x in Fig. 18. Shown also are the values of T c obtained from
the Gilleo theory (see discussion).
3.5.2 Crystallographic Data
The lattice constants for specimens in this system are listed in Table
VII and plotted vs x in Fig. 19. Shown also are the values obtained in
50
30
IP' 4
Xn
20
10
{Y 3 }Fe 5 -iAl x 12
1=3.0
^
rx=2.5
THEORETICAL
(FREE IONS)
2.0 Fe 3+ IONS
s
2.5 Fe 3+ IONS
1
SO 100 150 200
TEMPERATURE IN DEGREES KELVIN
250
Fig. 16 — Reciprocal susceptibility vs temperature for Y3Al2.sFe2.5O12 and
for Y,AliFcj0i2 .
BEHAVIOR OF SUBSTITUTED YKi
589
Table VII — Magnetic and Crystallograpiiic Data for Garnets
YjAUFe^Oia
«fl
7"c(°K)
fl(A)
Present Work
Ref. 4
Present Work
Ref. 4
Present Work
Ref. 4
0.00
0.33
0.07
1.00
1.50
1.67
1.75
2.00
2.33
2.50
3.00
3.00
5.00
5.01
1.73
0.94
0.55
0.15
-0.15(?)
-0.25(?)
4.96
3.50
1.63
430
365
295
240
545
497
415
12.376
12.311
12.276
12.256
12.239
12.206
12.164
12.161
12.376
12.353
12.331
12.306
12.265
12.215
12.159
12.003
the earlier investigation in these laboratories. Except for x = 1.00, the
latter values lie within individual experimental error on the curve given
by those more recently obtained and which are considered to be im-
proved. To a value of x = 2.5, the a vs x behavior of the Y 3 Fe5_xAl x Oi2
system is linear (and extrapolates to a value of 12.080 A for Y3AI2AI3O12) .
However, beyond this point, there appears to be an inflection toward
the abscissa. Two specimens with x = 3.00 were carefully prepared,
Fig. 17 — Spontaneous magnetization vs composition for aluminum-substi-
tuted yttrium iron garnets. (See text for explanation of values for x > 2.0.) Shown
also is the line expected, when ^ x ^ 1.0, if all Al 3 + ions replaced Fe s+ ions in
letrahedral sites.
51)0
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
bOO
■
^
{YafFes-a-AlxO.z
O PRESENT WORK
500
^x
A FROM REFERENCE 4
*~ N t*t = 0.825
400
*^
, ft = 0.765
N\i*
|0^ GILLEO MODEL
\ X
i
OBSERVED\
^ ft » 0.70
\
\
0.5
1.5
x
2.0
2.5
3.0
Fig. 18 — Curie temperatures vs composition for the aluminum-substituted
yttrium iron garnets. Shown also is the curve obtained from the Gilleo model
based on the distributions given in Fig. 29. The points denoted by crosses were ob-
tained from specimens in which Mg 21 " or Zr 4+ were substituted for Fe 3+ ions in octa-
hedral sites and Si* + for Fe 8+ ions in tetrahedral sites, with required electrostatic
balance by Ca 2+ ions in dodecahedral sites (see text).
12.4
12.3
Fig. 19 — Lattice constant vs composition for aluminum-substituted yttrium
iron garnets.
BEHAVIOR OF SUBSTITUTED YIG 591
one with ultra-pure A1 2 3 ; the lattice constants obtained for the two
specimens are 12.104 and 112.1 (>1 A (the latter for the ultra-pure speci-
men). The larger of the two values still is far from the straight line of
the first half of the system (Fig. 19). As will be shown in a subsequent
paper, a vs x for the GdaFeB-xAl^O^ system also does not behave exactly
linearly, although the inflection occurs at a much lower value of x.
IV. GENERAL DISCUSSION
The original purpose of this investigation was to test further the
Gilleo theory 3 and the extension thereof to substituted rare earth iron
garnets. 26 Following this paper, we shall publish one concerned with the
latter systems which will show, unfortunately, that this extension 25 of
the theory does not fit the results because, as the present paper will
show, the Gilleo theory for substituted yttrium iron garnets does not
fit the results. In fact, no existing theory accounts for the observations
quantitatively, and though the over-all agreement is rather poor, the
Gilleo theory comes the closest.
In this paper, we shall develop a descriptive theory for substituted
yttrium iron garnets which draws on various theories of Neel, 26 Yafet
and Kittel, 5 Gilleo 3 and Anderson. 27 The possibility of a quantitative
theory which can predict the magnetic behavior of the substituted
garnets is complicated by the various effects of substitution on the
magnetic structure. These effects appear to be more complex for higher
substitution, and in fact there is now evidence that, especially for high
substitution, different nonmagnetic ions in the same site produce different
behavior (see also Refs. 10-13 and Section 4.3). In a sense, this is a
rather unfortunate result because, before we discovered it, we believed
that even without a quantitative theory, we should be able from limited
data to predict the magnetic behavior of any substituted yttrium iron
garnet. Actually, as will be shown later, this can still be done within a
certain range of substitution and for particular ions.
The present data strongly indicate that the Si 4+ ion has a preference
exclusively for tetrahedral sites in the garnets. 28 The preference of the
Ge 4+ ion for tetrahedral sites is not quite as great as that of the Si 4+ ion;
that is, with increasing Ge 4+ ion substitution, there does appear to be
some tendency for a small percentage of these ions to go into octahedral
sites. However, this percentage is not nearly as large as previously 21
indicated.
Assuming that our present conclusion regarding the site preference of
the Si ion is correct, we may compare Fig. 4 with the observed data,
592 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
n B (0°K) vs x calculated on the basis of a simple N6el model 26 and on
that proposed by Gilleo. 3 It is seen that neither model gives satisfactory
agreement with the observations over the whole range of substitution.
In the range to x « 1 .9 there is apparently better agreement with the
simple Neel model than with the Gilleo one. The observed minimum,
-3.85 (x B , occurs at X = 1.94; the minimum predicted by the Gilleo
model is -1.8 m« at x = 1.77; the Neel theory does not predict a mini-
mum, but does not preclude one (see Section 11 of Ref. 26). Agree-
ment of observed 0°K moments for octahedral substitution (see Fig. 7)
with those calculated with the Gilleo theory is somewhat better than
for tetrahedral ion substitution, but it cannot be said to be satisfactory.
For the { Y 3 }[Mg I Fe 2 -x](Fe 3 -xSix)0, 2 system (see Fig. 11), the moments
calculated with the Gilleo theory are also not in good agreement with
the observed values. Thus, although the Gilleo theory predicts a maxi-
mum for octahedral and a minimum for tetrahedral substitution, it
does not appear to account quantitatively for the observed moments in
any of the systems. It should be pointed out, however, that unlike others,
this theory takes into account the statistical nature of the problem,
while on the other hand it has neglected the importance of intrasub-
lattice interactions.
Wojtowicz 29 has shown that intrasublattice interactions are negligible
in the (unsubstituted) yttrium and lutecium iron garnets, while the
results of Pauthenet 7 and of Aleonard 30 based on the Weiss molecular
field theory (as applied by N6el to ferrospinels) show that they are
important. The theory of Yafet and Kittel, 5 also based on the Weiss
molecular field theory, leads to the result that at a certain concentra-
tion of nonmagnetic ions in a particular site in a ferrospinel, a transition
occurs to a ground state in which there is canting of moments in the
unsubstituted sublattice. We shall show below that this theory also
does not account for the behavior of the substituted garnets. Neverthe-
less, an important implication of our structural argument is the impor-
tance of intrasublattice interactions.
As indicated earlier, there is an arithmetic error in the de Gennes
application 6 of the Yafet-Kittel theory to the Sn 4+ ion substituted
garnets: the molecular field equations for YIG determined by Pauthe-
net 7 should have been written
II A = -7000 M A - 14,800 Mb
H B = -14,800 M A - 4200M B
from which n = +14,800, « 2 = -0.95, 72 = -0.57. Thus according to
the theory it is at y - 0.57 or x = 0.29 that the canting first occurs.
BEHAVIOK OF SUBSTITUTED YIG 593
Also, the maximum moment, 6.45 hb , in the system should then be
attained at x = 0.29. Actually, if this system is assumed to behave
similarly to those of Fig. 7, the maximum moment of 7.8 /x« is attained
at about x = 0.7 and the canting appears experimentally to occur earlier
(see later discussion).
But the discrepancies for the silicon-substituted yttrium iron garnet
are even worse. Again using the Pauthenet equations, the triangular
configuration (c) of the Yafet-Kittel theory would be expected, that is,
for 1/ | a-i | < //. The system is \ Y :i _. r Ca. f |[Fe2](Fe3-,Si. r )Oi2 ; thus y =
2/(3 — x). Canting should therefore begin at X = 1.1. For x < 1.1,
n B (0°K) = 5(1 - x) while for x > 1.1,
n fl (0°K) = 5(3 - .r)(l - 1/ | a 2 | ) = -0.25(3 - x).
The algebraic minimum, —0.5 n„ , should occur at x = 1.1 ; the observed
values are —3.85 /x fl at x = 1.94.
For the |Ca;i|[Fe 2 ](Si;i)Oi2 specimen, the value of \/xo in units com-
parable to those used by Aleonard, is —1.9. Thus n a „ = —1.9, which
is about Y2 the value of n aa in YIG. This value of n aa indicates very weak
magnetic interaction in line with the 6 P of 29°K and the possible Neel
temperature of 9°K and also implies that the interaction coefficients
change with substitution. Thus it appears that the use of the interaction
coefficients of YIG to predict the behavior of the entire system is not
correct.
In a first approximation, it appears now that the following picture of
the behavior of the substituted yttrium iron garnets (discussed in this
paper) is a plausible one. Yttrium iron garnet itself may be considered
an ideal N6el ferrimagnet ; that is, at 0°K, the moments of all a-site
Fe 3+ ions are exactly parallel, the moments of all <7-site Fe 3+ ion moments
are exactly parallel and the moments of a-site Fe ions are exactly
antiparallel to those in the r/-sites. Under these circumstances the the-
oretical moment, 5.0 ix H per formula unit, should be and is observed.
When the (/-sites are filled with nonmagnetic ions, as in Ca3Fe 2 Si 3 0i2 ,
at the very least, short-range antifcrromagnetic order occurs among the
moments of the a-site Fe 3+ ions. When the a-sites are filled with non-
magnetic ions, as for example in hypothetical { YCa2}[Zr 2 ](Fe3)Oi2 , at
the very least, short range antifcrromagnetic order occurs among the
moments of the r/-site Fe 3+ ions ( see also Ref . 27 ) .
Thus, on a structural basis, replacement of Fe 3+ ions in a particular
site by nonmagnetic ions must ultimately change a ferrimagnetic to
some type of antiferromagnetic structure. Figs. 4 and 7 show that this
occurs continuously; Figs. 20 and 21 show the connection between the
594
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
Fig. 20 — Continuous relation between the Bystemfl ( Ys-xCax} [Fe 2 ](Fej_xSix)Oi2
and |Y3_xCaxl[Zr I Fe 2 _x](Fe 3 )Oi2.
silicon- and zirconium-substituted yttrium iron garnet systems and give
a pictorial summary of the behavior of these systems. Now, let us assume
(see Fig. 21) that in the silicon-substituted garnets at 0°K, only the
effective moment 31 of the octahedral Fe 8+ ion sublattice is reduced by
canting of the moments of these ions because of linkages to tetrahedral
nonmagnetic ions and the effect of a-a antiferromagnetic interaction.
Analogously, we assume (see Fig. 21 ) that in the zirconium (or similar)
ion substituted garnets, only the effective moment of the tetrahedral
Fe 8+ ion sublattice is reduced. We can then determine the average
effective 31 moment per octahedral and per tetrahedral Fe ion, respec-
tively, as a function of x. The results (Fig. 22, curves 1 and 4) indicate
that far more silicon than zirconium substitution is always required to
cause reduction of the average Fe 3+ ion moment in the octahedral and
tetrahedral sublattice, respectively.
A small part of the arrangement of cations in the a and d sites of a
zirconium-substituted garnet crystal is shown in Fig. 23. For further
clarity, we show in Fig. 24 the arrangement of cations in the three types
of sites in four octants of the garnet unit cell. In yttrium iron garnet, 32
each ion on an a site is linked through pairs of oxygen ions to eight
a-site ions at distance 5.36 A and through single oxygen ions to six
tf-site ions at 3.46 A. Each rf-site ion is linked through pairs of oxygens
to four rf-site ions at 3.79 A and through single oxygens to four a-site
ions at 3.46 A. These distances and linkages through oxygen ions imply
BEHAVIOR OF SUBSTITUTED YIG
595
C.N. 8 6 4
{c} [a] (d)
DOD. OCT. TETR.
(stn
SHORT AND LONG RANGE CHEMICAL ORDER
{Y 3 }[Fe 2 ]fFe 3 )0 12
IDEAL FERRIMAGNET
SHORT AND LONG RANGE MAGNETIC
ORDER
[Zr«1
SOLID SOLUTION
LONG RANGE CHEMICAL ORDER ONLY
{ Y 3-xCa I }[Fe 2 ](Fe 3 . ;p SL I )O l2
( t
FERRIMAGNET WITH RANDOMLY
CANTED a-SITE Fe 3+ ION MOMENTS
LONG RANGE MAGNETIC ORDER ONLY
SOLID SOLUTION
LONG RANGE CHEMICAL ORDER ONLY
{Y3-xCa a .}[Zr I Fe 2 . a .](Fe 3 )0 12
I >
FERRIMAGNET WITH RANDOMLY
CANTED d-SITE Fe 3 " 1 " ION MOMENTS
LONG RANGE MAGNETIC ORDER ONLY
(Sl" + )
[Zr 4+ ]
SHORT AND LONG RANGE CHEMICAL ORDER
{ca 3 }[Fe 2 ](si 3 )o 12
AT LEAST SHORT RANGE ANTIFERROMAGNET
LONG RANGE CHEMICAL ORDER
{YCa 2 }[Zr 2 ](Fe 3 )0 12
AT LEAST SHORT RANGE ANTIFERROMAGNET
Fig. 21 Summary of proposed explanation for the magnetic behavior of the
systems |Yj_Cax)lFoB](Fe3_Si,)()| 2 and |Yj_ I Ca,}[Zr«Fe«_](Fe 3 )Oia .
that in YK1 the a-d interaction should be strongest, next the d-d and
finally the a-a.
The results shown in Fig. 22 indicate that the average a-d interaction
weakens as substitution of nonmagnetic ions is made in either site.
Nevertheless the a-d interactions remain dominant until the changes in
direction of the curves are reached. At .<„ = 0.70, a transition occurs to a
state in which the d-d interactions are dominant. 3 ' 1 Similarly at x t = 1 .92,
a transition occurs to a state in which the a-a interactions are dominant.' 1 ' 1
Because the transition occurs for x t = 1.92 as against x„ = 0.70, there
is little question that the d-d interactions in the Zr 4+ ion substituted
garnets are stronger than the a-a interactions in the Si 4+ ion substituted
system. Moreover, as shown in Fig. 25, the ratio of Xt/x required to
reduce the effective Fe ion moment to a particular value is everywhere
greater than 1 .75.
The decreases in effective moments of the sublattices with increasing
x are small but real until the transition points are reached. However, it
590
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
z
O 5
Z 3
2
§ 2
^^■^s
\ 4
s. ^
\v 2 ^
1 \
\
0.4 0.8 1.2 1.6 2.0 2.4 2.8
Fig. 22 — "Effective" moment (see Ref . 28) per Fe 3+ ion in (1) tetrahedral
sites for {Ya_ I Ca I )[Zr I Fe2_x](Fe 3 )0,2 system; (2) tetrahedral sites for
|Y 3 }[ScxFe 2 _x](Fe3)Oi2 system; (3) tetrahedral sites for (Y 3 l[MgxFe2_x]-
(Fe 3 _xSix)Oi2 system; (4) octahedral sites for j Y 3 _ I Ca I )[Feo](Fe 3 _xSix)0 12 system.
Circle points are for lY3-xCax)[ScxFe2-x](Fes_xSix)Oi2 specimens and triangles for
(Y 3 _2xCa2x|[ZrxFe 2 _x](Fe 3 _xSix)Oi2 specimens (see text).
would appear from the Yafet-Kittel theory that if there were no short-
range disorder, there should actually be no decrease in effective moments
before the transitions are reached, since the ground state before the
transition should be an ideal ferrimagnetic one, with no splitting of the
sublattices. That is, because the a-d interactions are dominant, the
molecular field of the d sublattice, in the case of tetrahedral substitu-
tion, would act to keep the a sublattice moments aligned antiparallel to
the d; while in the case of octahedral substitution, the molecular field
of the a sublattice would act to keep the d sublattice moments aligned
antiparallel to the a. On the other hand, it would appear that chemical
disorder which always exists in a solid solution would cause magnetic
disorder. This chemical disorder implies further that distinct "sublattice
splitting" does not really occur in these substituted garnets, but rather
that the canting of the moments within a sublattice is random, and that
since the crystals are ferrimagnetic, a statistical long-range order must
exist.
We see also in Fig. 22 that although until the transition points are
reached the rates of decrease in effective moments of the sublattices
with increasing x are both small, that for tetrahedral substitution is
BEHAVIOR OF SUBSTITUTED YIG
597
(D Fe 3+ ION in a
O Fe 3+ ion in d
Fig. 23 — Part of the arrangement of cations in the a and d sites of a zirconium-
substituted yttrium iron garnet crystal.
much smaller than for octahedral substitution. This shows again that
the d-d interactions are stronger than the a-a. Now it is unlikely that
short-range magnetic disorder occurs before the transition and not be-
yond it. Thus it appears that what is occurring differs from the idealiza-
tion given by the Yafet-Kittel theory. The transition is almost surely
one at which a change from dominance of the a-d to a-a or d-d inter-
actions occurs, but not one in which there is an abrupt change from a
strictly ferrimagnetic to a canted ground state. That is to say, there is
always a competition among the various interactions, and as soon as
the strictly antiparallel one is disrupted, one of the others may begin to
manifest itself.
To emphasize at this point the importance of the competing inter-
598
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
Fig. 24 — Arrangement of cations in r, a, and d sites in four octants of the
garnet unit cell.
actions, we outline some further evidence to be discussed in more detail
later. Suppose we look at a system in which substitution of nonmagnetic
ions is made in both sites. We choose ions such as Sc' i+ and Si 4 which we
believe have exclusive preference for octahedral and tetrahedral sites
respectively. A formula representing such a system is j Y 3 _ J ,Ca // i [80^62-*]-
(Fe 3 _„Si„)Oi2 . Suppose we begin with .// = and x = 0.30. We see from
Fig. 22 that some canting will occur among the Fe 3+ ion moments on
the tetrahedral sites. Now we keep x constant and increase y. As y
increases, the canting of the rf-site Fe 3+ ion moments will decrease. A
value of y will be reached for which the particular garnet will again
appear to be an ideal Neel ferrimagnet. The value of y for which this
occurs (see Table V) is 1.52, that is to say, for the garnet {Y1.4sCa1.52}-
[Sc .3oFei.7o](Sii.52Fei.4 8 )Oi2 . For this garnet, the difference in the num-
ber of Fe 3+ ions in the two sites is 0.22, which according to the Neel
model would give a 0°K spontaneous magnetization of — 1.10 Mb 5 the
BEHAVIOIt OF SUBSTITUTED YIG
599
*0
5
0.5
1.0 1.5
2.0
\
4
\
\
3
2
EFFECTIVE MOMENT PER Fe ION IN /i B
Fig. 25 — The ratio, x t /x„ , of tetrahedral to octahedral nonmagnetic ions,
required to produce the same effective moment per Fc 3+ ion in the appropriate
sublatticc. Also shown is the curve xt/x a vs j„ .
observed value, —1.12 fi H , is in good agreement with this value. Note
(Table V) that for the garnet |YijiGai^r}^0B.»Fei.y](Sii^irFeiji)Ois l
the observed ()°K spontaneous magnetization is —0.92 \i u , to be com-
pared with —5 X 0.17 = -0.85 n„ from the Neel model. Thus for this
garnet canting of the Fe ion moments occurs in the tetrahedral sites.
On the other hand, in the case of the garnet [Y1.4Ca1.6HSco.3Fe1.7l-
(Sii.eFei .4)012 , the observed ()°K spontaneous magnetization is —1.39
/j B , to be compared with — 5 X 0.30 = —1.50 n„ from the Neel model.
Thus for this garnet canting of the Fe 3+ ion moments occurs in the
octahedral sites. (This example also demonstrates that the 0.3 Sc 3+
ions are in octahedral sites exclusively. )
The above discussion has been concerned only with what occurs at or
very near 0°K. It appears, however, that the behavior of these sub-
stituted garnets may be similar at higher temperatures. We note (see
Fig. 5) that .v t /.r required to give the same Curie temperature is every-
where greater than 1.(18. Fig. "> also shows the effect of transition from
a-d to intrasublattice interaction dominance, even though, except for
the Y 3 [Mg. r Fe2-.r](Fe3_. r Si. r )Oi2 systems, it does not show as clearly as
Fig. 22 where the transition values of x are.
600 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
Also shown in Fig. 5 is the plot of T c vs x obtained from the Gilleo
theory. The agreement with observed Curie temperatures is rather
good; for the | Y 3 )[Mg x Fe 2 _ x ](Fe 3 _ x Si x )0 12 system, it is almost perfect.
Thus it is possible that, although the Gilleo theory does not hold at low
temperatures, it does at higher temperatures. However, it is also possible
that this good agreement of Curie temperatures is fortuitous (see later
discussion).
In the system {Y 3 !lMg x Fe 2 _ x ](Fe 3 _ x Si x )Oi 2 there is always 1.0 more
Fe 3+ ion per formula unit in the tetrahedral than in the octahedral
sites. Thus the apparently continuous decrease in total 0°K moment
(Fig. 11) in the early stages of substitution must, according to our
model, mean that canting of the Fe 3+ ion moments is occurring in the
tetrahedral sites. If we assume that the moments of the a-site Fe ions
remain parallel we may determine for each composition the effective
moment contributed to the ferrimagnctism by each tetrahedral Fe
ion, as shown in Fig. 22, curve 3.
We note that there are two main regions of behavior similar to those
in the systems in which substitution of nonmagnetic ions is made ex-
clusively either in octahedral or in tetrahedral sites. The decrease in
effective moment (or increase in canting) is initially at the same rate as
in the {Y 3 _ x Ca x l[Zr x Fe 2 _ x ](Fe 3 )0, 2 or ( Y 3 }[Sc x Fe 2 _ x ](Fe 3 )Oi 2 systems,
but beyond x tt 0.7 the rate of decrease of effective moment is lower than
in the latter system. Thus we conclude tentatively (see later discussion)
that:
( 1 ) canting of Fe' l+ ion moments in the tetrahedral snblattice occurs
from the beginning of substitution;
(2) in the region < x ^ 0.7, the replacement of d-site Fe 3+ ions by
Si 4+ ions does not have a significant effect on the average d-d interaction
strength, but when x > 0.7, decreases the average d-d interaction
strength ; thus
(3) in the 1 Y 3 )[Mg x Fe 2 _ x ](Fe 3 _ x Si x )(),-. system, the transition to the
dominance of the d-d interactions over the a-d interactions (see Ref. 33)
occurs at x « 0.95 as against x = 0.70 in the | Y 3 _ x Ca x ) [Zr x Fe 2 _ x ](Fe 3 )Oi 2
system.
The Curie temperatures of the { Y 3 |lMg x Fe 2 _ x ](Fe 3 _ x Si x )Oi 2 system
are shown in Fig. 5 (curve 1 ). The latter are almost everywhere smaller
than those of the {Y 3 } [Sc x Fe 2 _ x ](Fe 3 )0, 2 system for the same x. However,
the differences are nowhere greater than 35°K even though x in the
{Y 3 }[Mg x Fe 2 _ x ](Fe 3 _ x Si x )Oi 2 system represents as many nonmagnetic
ions in d as in a sites, or twice as much total substitution of nonmagnetic
ions. This comparison already indicates that the canting may also have
BEHAVIOR OF SUBSTITUTED YIG
601
an effect on the Curie temperature; that is, that the intrasublattice
interactions arc important over a wide temperature range and not only
atO°K.
We may obtain a clearer idea of the effect of the intrasublattice inter-
actions on the Curie temperatures by plotting T c vs total per cent
substitution of nonmagnetic for Fe + ions as in Fig. 26 for exclusively
a-site, rf-site and equal a-rf-site substitution. Now we see that on this
basis, the Curie temperatures for the [Y; i }[AIgxFe2- J .](Fe; i _ J .Si x )Oi2 sys-
tem are everywhere substantially greater than those for the
{ Y ;t J[Sc I Fe2- 3 :](Fc3)Oi2 system for the same total per cent replacement of
Fe 3+ ions. Further, to about 37 per cent substitution, the values of T c
for the Y:t[Mg,Fe 2 _x](Fe 3 _ x Si x )Oi2 system are lower than for the
{Y 3 _ I Ca J .|[Fe2](Fe3-iSi I )Oi2 system. (The actual values of x are
about 0.9 and 1.85 for the systems, respectively.) In the region
below 37 per cent substitution, canting of rf-site moments in
the former system is greater than canting of a-site moments
in the latter (Fig. 22). In the region above 37 per cent the
<a 300
d )Y 3 }[sc a: Fe 2 .J(Fe3)o 12
A {Y 3 }[Mg :E Fe 2 . a; ](Fe3. :c Sl a .)0 12
o {Y 3 _ ;c Ca ;c }[Fe 2 ](Fe3. x SL a ,)0 12
25 50 75 100
TOTAL PER CENT REPLACEMENT OF Fe 3+ IONS
Fig. 26 — Curie temperatures vs total per cent replacement of Fe 3+ ions.
602 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
reverse is true. For example, for 50 per cent substitution the formulas
are respectively YslMgi.asFeo.wKFei.TBSii.aOOM and { Y . 5 Ca 2 .5} [Fe 2 ]-
(Feo.5Si 2 .5)0]2 ; Fig. 22 shows that the effective moment of the d-site
Fe 3+ ion in the former is 3.35 p. B while that of the o-site Fe 3+ ion in the
latter is 1.6 /x B . [Thus we see also why even when there are only 1.8
Fe 3+ ions left per formula unit, i.e., {Y 3 }[Mgi. 6 Feo.4](Fe 1 . 4 Sii.6)Oi 2 , we
still have a ferrimagnetic specimen with T c = 50°K. In fact, even when
x = 1.7 (1.6 total Fe 3+ ions per formula unit), the garnet may still be
ferrimagnetic]
We should expect that in the general system { Y 3+ x-«Ca y _x} [Mg x Fe 2 _ :c ]-
(Fe 3 _ J/ Si J/ )Oi2 there will be, for a given (x + y), a value of x
(or ft = y/x + y) such that there will be no canting of Fe 3+ ion mo-
ments in either sublattice. We saw above for x + y = 2.50 (50 per
cent substitution) that the effective moments when x = y = 1.25
(ft = 0.5) and when x = 0, y = 2.50 (ft = 1.0) are both lower than
5.0 hb . Because canting occurs in different sublattices for these two
garnets, the garnet in which no canting will occur [for this value of
(x + y)] should have 0.5 < ft < 1.0. Moreover, this garnet should
have the maximum Curie temperature for x + y = 2.50. We have not
attempted to obtain this particular garnet, but in the course of our
investigations we have made one very close to it. The garnet with for-
mula }Y 2 Ca}[Mgo.76Fei. 26 ](Fe 1 . 25 Sii. 7 5)Oi 2 (f t = 0.70) has a 0°K mo-
ment of —0.18 hb (Table V). Our accumulated data indicate that
the canting occurs in the tetrahedral sites (the octahedral sublattice
then dominates, therefore the choice of negative sign); the effective
moment of a tetrahedral Fe 3+ ion is 4.85 /i* • The Curie temperature
is 250°K; for/, = 0.50 and 1.00, the Curie temperatures (see Tables I
and IV, respectively) are 187 and 86°K respectively. It is also note-
worthy that the garnet with /, = 0.70 saturates at low temperatures
at about 10 koe, whereas the other two do not.
In the foregoing discussion, it would appear that it was tacitly assumed
that the 0°K moments and Curie temperatures do not depend signifi-
cantly on the type of nonmagnetic ion substituted for the Fe 3+ ion in
yttrium iron garnet. That is to say, it would appear that we had im-
plied that a garnet such as {Y 3 -x-uCa x+ y}[Zr x Fe2- x ](Fe 3 - v Siy)Oi2 will
have the same 0°K moment and Curie temperature as
{ Y a - v Ca v } [ScxFe 2 _*] ( Fe 3 -A ) 12
or as {Y 3+ x-i,Ca I/ _ I }[Mg I Fe2-x](Fe 3 _„Si y )Oi2 provided all x's are the
same and all y's are the same. This appears to be a generally accepted
idea.
BEHAVIOR OF SUBSTITUTED YIG 603
However, there now appeal's to be some evidence that this is not
generally true (see also Refs. 10-13 and Section 4.3). In Fig. 7 and
Table III, it will be noted that beyond about x = 0.7 the moments
for the system jY3_ J .Ca J -}[Zr J Fe2-i](Fe 3 )Oi2 are lower than those for
the system { Y 3 |[Sc r Fc-.>-. r ](Fe3)Oi; ! . The differences are outside experi-
mental error. We shall discuss substituted gadolinium iron garnets
fully in a future paper, but as further evidence of the reality of the
differences in the two systems we point out here the moments obtained
from high-field measurements at 4.2°K of |(ld.iCa}[ZrFe](Fe:i)Oi 2 and
((Jd,Y|[ScFe](Fe :i )() 12 . Extrapolation of n H (II„) vs //„ to //„ =
gives 5.3 and 4.0 y. R for these, respectively. Extrapolations of n B (H a ) vs
\/H a to \/H n = give 7.1 and (>.7 m» for these respectively. Regardless
of which values are more nearly the correct ones for these garnets, the
moment of the Zr-substituted gadolinium iron garnet is significantly
higher than that for the Sc-substituted one. Because the net moments
from the iron sublattices of these garnets are antiparallel to those of
the gadolinium sublattices, the net moment per formula unit of the
Zr-substituted gadolinium iron garnet should be larger than that of the
Sc-substituted gadolinium iron garnet, if the moments of the analogous
substituted yttrium iron garnets are in the reverse order.
One may well ask whether these differences are a result of some
Zr or Sc' 1 ions being in tetrahedral sites. While this possibility cannot
be completely eliminated, evidence will be presented which indicates
that it does not account for the results. Now, the Zr ion is a rather
large one; in ZK) 2 it prefers eight-coordination,' while in zirconates it
prefers six-coordination. Lower coordination for Zr has, as far as we
know, not been reported, although there is no a priori reason to deny
its possibility. If we, however, assume that all Zr ions go into octa-
hedral sites in the garnets, we may ask if some Sc 3+ ions go into tetra-
hedral sites. Consideration of this possibility leads to the conclusion
that if some Sc' 1+ ions do go into tetrahedral sites, the percentage doing
so decreases to a minimum and then increases again.
We arrive at this conclusion in the following way. We assume that a
small amount of Sc 3+ ions in the tetrahedral sites does not alter the ef-
fect of the presence of the large amount of Sc + ions in octahedral sites
on the moments of the Fe 3+ ions in the tetrahedral sites. Thus for one
Sc 3+ , if we assume a formula of |Y 3 }[Sco.9Fei.i](Fe2.9Se n .i)Oi2 , the
effective moment (Fig. 23) of a tetrahedral Fe 3+ ion will be 3.85 ti B .
The 0°K spontaneous magnetization per formula unit would then be
5.7 hb , in agreement with the observed value. A distribution given by
( Y3)[Sco.95Fei.o5](Fe 2 .95Sco.o5)Oi2 gives a moment per formula unit of
604 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1904
5.4 hb . For 1.25 Sc 3+ ions with a distribution given by {Y 3 }[Sci. 2 Fe .8]-
(Fe 2 .95Sco.o5)0 12 , the effective tetrahedral Fe 3+ ion moment is 2.43
/x fl and the 0°K moment per formula unit is 3.1G n B , which is in good
agreement with the observed value. The distribution {Y 3 }[Sci.i 5 Fe . 8 5]-
(Fe 2 .9oSco.io)Oi2 , however, leads to a 0°K moment per formula unit of
3.4 hb • For 1.50 Sc 3+ ion with a distribution given by {Y 3 }[Sci. 4 Feo. 6 ]-
(Fe 2 . 9 Sco.i)Oi 2 , the derived 0°K moment per formula unit is 1.4 n B ,
in agreement with the observed values.
One can see then from these examples that if the assumptions were
correct, the percentages of Sc 3+ ions entering tetrahedral sites would
be 10, 4 and G.7 respectively. Such a situation is felt to be rather un-
likely; one would expect the fraction of Sc 3+ ions going into tetrahedral
sites to increase monotonically. Under such conditions, the curves
of Fig. 7 for the Zr- and Sc-substituted yttrium iron garnets should
actually cross at a value of x > 0.70. It is still possible that very small
amounts of Zr 4+ ions may go into tetrahedral sites, in which case, if
Sc 3+ ions also go into tetrahedral sites, the situation would be more
complex; but there is further evidence that this alone would still not
account for the observations.
Fig. 4 indicates a resemblance of the behavior of the Ge- and Si-
substituted yttrium iron garnets to those of the Zr- and Sc-substituted
garnets. At x > 1.0, the 0°K moments per formula unit (absolute
values) of the Ge-substituted garnets are lower than those for the Si-
substituted garnets. Now, in Figs. 7 and 23 and Table III it will be
noted that to x = 0.70 the Zr and Sc-substituted garnet systems behave
in very nearly the same way. Below x = 0.70, it is expected that all
these garnets will saturate magnetically at moderate fields. It is mainly
in the region in which the intrasublattice interactions become dominant
that substantial differences occur (but see Refs. 10-13 and Section 4.3);
this is the region in which saturation is not attained at fields to 80 koe.
As pointed out earlier, it is now felt that it is unlikely that Si 4+ ions
enter the octahedral sites in the garnets. Thus it may be concluded that
because between x tt 1.0 and 1.92 the Ge-substituted garnets have
lower moments (absolute values) than the analogous Si 4+ ion substituted
garnets, some Ge 4+ ions do enter octahedral sites. When x = 1.00, the
distribution of ions is probably given by {Y2CajfFe1.99Geo.01]-
(Fe 2 .oiGeo.99)0, 2 . When x = 1.92, the distribution is probably given by
{Y 1 .o 8 Cai.9 2 }[Fe 1 .94Geo.o6](Fe 1 .i4Ge 1 . 8 6)Oi 2 . However, if the percentage
of Ge entering octahedral sites increases with increasing total substi-
tution, and if there are no other effects on the spontaneous magnetization
resulting from the particular ion, the curve for Ge substitution should
cross that for Si substitution.
BEHAVIOR OF SUBSTITUTED YIG 605
If, for the sake of discussion, a linear relation between percentage
Ge in octahedral sites vs total Ge substitution is assumed for x > 1.0,
the distribution for x = 2.0 would be given by jYCa2KFe1.93Geo.07]-
( Fei .07Gei .93 ) O12 and f or
x = 2.25, {Yo.75Ca2. 25 }[Fei.9iGeo.o9](Feo.84Ge2.i6)Oi2 .
Using Fig. 22, the effective moments of the octahedral Fe 3+ ions would
be 4.70 and 3.40 y, H respectively. The 0°K moments then should be
—4.0 and —2.3 \i B respectively, as compared with the observed values
— 3.15 and —1.55 /*» respectively. Note (see Fig. 4) that the observed
value for 2.0 Si is —3.8 \i B . It is probable that for x = 1.92 there is
somewhat less than 0.06 Ge in octahedral sites, but regardless of the
actual amounts, the single assumption of some Ge + ions in octahedral
sites cannot account for the observations if it is also assumed that Si 4+
ions go only into tetrahedral sites in the garnets. But even if the latter
assumption were unacceptable, it is certain that the Si 4+ ions would
have a greater preference for the tetrahedral sites than Ge 4+ ions.
And it would then still appear necessary for the Ge curve to cross the
Si curve if there were no additional effect resulting from the substi-
tution of a particular ion.
This conclusion also is perhaps contrary to the thinking on ferri-
magnetic materials. Generally, it is believed that for a given total
substitution, when the net difference in the number of Fe 3+ ions is
greater, the moment per formula unit should be greater. However,
there is concrete evidence that the conclusion is correct.
This may be illustrated by the following example. The garnet
{Yi. 2 40ai.76}[Mgo.22Fei.78](Fei.o2Sii.98)Oi2 has a 0°K moment of —3.1
Ms 35 and a Curie temperature of 245°K. The garnet j Yo.8Ca 2 .2)[Fe 2 ]-
(Feo. 8 Si2.2)Oi2 has a 0°K moment (see Fig. 4) of —2.3 /*« and a Curie
temperature (see Fig. 5) of 200°K. (Note that the difference in the
number of Fe 3+ ions in the former is 0.76 and in the latter 1.2.) If it is
again assumed that the tetrahedral Fe 3+ ion moments remain parallel,
then in the former the effective moment of an octahedral Fe 3+ ion is
4.5 hb ■ Examination of Fig. 22 shows that this is just slightly larger
than the effective moment of the octahedral Fe + ion in {Y1.02Ca1.93}-
[Fe 2 ](Fei.o2Sii.9s)Oi2 . The 45°K lower Curie temperature of (Y .8Ca 2 . 2 }-
[Fe2](Fe„. 8 Si2.2)0 12 than that of |Y, .24Ca. 1 . 7 «}fMgo. 22 Fei.78](Fe,.o 2 Si,.98)0 12
is in accord with the stronger interactions in the latter. The Curie
temperature of the latter is 25°K lower than that of {Yi.o 2 Cai.9 8 )[Fe 2 ]-
(Fei.o2Sii.98)Oi2 (Fig. 5), which has a larger number of interactions of
about the same strength.
The effects of different ions on magnetic behavior are more marked
606
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
in several of the specimens shown in Tables IV and V. The systems
involved are |Y 3 _ J/ Ca tf |[Sc J Fe 2 _,](Si tf Fe 3 -x)Oi 2 , { Ys-.+.Ca,,-*} [MgzFe^J-
(Si„Fe ;i _ w )Oi2 , and {Y 8 _ s _„Ca !C+1 ,}[Zr x Fe2-x](SiyFe 3 - 1 ,)Oi2 . The results
for specimens with values of x and y: x = y = 0.85; x = y = 1.00;
x = 0.90, y = 1.10; and x = 1.10, // = 0.90 are retabulated in Table
VIII. In the last case, it is not now possible to prepare the specimen
in which M = Mg 2+ because electrostatic balance with a tetravalent
ion in the c-sites would be required. It is seen that the moments and
Curie temperatures decrease in the order Mg, Sc, Zr and that satura-
tion is more easily attained in those garnets containing magnesium
than in the others. If we assume for the time being that all the Mg
ions go into octahedral sites, it appears that if it were possible to find
a tetravalent ion to balance electrostatically the Mg 8 ions as in a
hypothetical system | Y a _ J AW + )[Mg/ + Fe 2 _x](Fe :t )0 12 , the effective
moment of a tetrahedral Fe 3+ ion for given x would be higher than for an
analogous Sc 3+ -substituted yttrium iron garnet. This, of course, neg-
lects any effect that the ions substituted in the c-sites would have on
the magnetic structure. There are probably effects of the c-site substi-
tuted ions, 13 but it is impossible to determine them for divalent ions
such as Ca 2+ separately. It should be pointed out that when x = y
no substitution for Y is necessary when M = Mg 2+ ; x Ca 2+ is necessary
when M = Sc 3+ , and 2x Ca 2+ is necessary when M = Zr .
The important question again arises: are some of the ions assumed
to be in octahedral sites actually in tetrahedral sites? To try to answer
this question directly, we have taken quantitative x-ray intensity data
Table VIII — Retabulation of Data from Selected Specimens
from Tables IV, V and VI
" H
H a =
Saturation Field,
Octahedral Ion
Tc , °K
koe
x = y =
0.85
Mg
4.25
327
11.3
Sc
4.0
12.6
Zr
3.6
70
x = y =
1.00
Mg
3.8
2(35
70
Sc
2.9
235
>70
Zr
2.1
200
>70
x = 0.00, y
= 1.10
Mg
3.2
294
9.(3
Sc
2.8
260
>70
Zr
1.9
210
>70
x = 1.10, y
- 0.90
Sc
2.8
220
>70
Zr
1.8
190
>70
BEHAVIOR OF SUBSTITUTED YIG 607
from the specimens of (Yo.BCaa.6}[Zri.26Feo.7B](Fei.7jSii.26)Oij and
{Y 3 }[Mgi.86Feo.i6](Fei.iBSii.85)Oi2 . The data were collected with the
Norelco powder diffractometer using CuK a radiation. Integrated
intensities were measured on the charts with a Keuffel and Esser polar
planimeter. In the calculations of intensities, corrections were made for
anomalous dispersion, 36 the imaginary parts being included. 37 Estimates
of oxygen ion positions were as far as possible based on interatomic
distances expected between the ions involved. Calculations were made
for the above distributions and also for {Yo.6Ca2.6}[Zri.ooFei.oo]-
(Fei.6 Zro.25Sii.26)Oi2 and (YaHMgi.voFeo.soKFei.oMgo.^Sii^O^ .
The results indicated that the x-ray data cannot give unequivocal
conclusions regarding the exact distribution of the ions in these gar-
nets. However, the assumptions that the Mg J+ and Zr 4+ ions substitute
only in the octahedral sites in the two garnets are certainly compatible
with the data. Furthermore, examination of powder photographs of
related garnets indicates that it is more likely that the Zr + and Mg 2+
ions prefer octahedral sites exclusively than that some enter tetra-
hedral positions.
If, however, we examine the Curie temperatures in each x,y (for
•'" + .'/ = 2.0) group of Table VIII, we might be led to believe that if
all Zr 4+ ions are considered to be in octahedral sites, because substitution
in the octahedral sites has a far greater effect on Curie temperature than
tetrahedral substitution in this region of x and //, some Sc 3+ ions go into
tetrahedral sites and more Mg 2+ ions do. On the other hand, we note
that for Zr + ion substitution the highest moment is obtained for
x = y = 1.00, those for x = 0.90, y = 1.10 and z = 1.10, y = 0.90
being lower. In fact, the same seems to be true for Mg 2+ and for Sc 3 '
substitution. It thus appears unlikely that the results can be explained
on the basis that the distributions of ions are different from those as-
sumed.
To examine this conclusion further, we note the results on several
other specimens. Table VI lists some (le 4 + ion substituted specimens
analogous to those in Tables IV and V. For YaMgFesGeO^ , YjMgi . 2 &-
Fc2.r,(i(iei.250i2 and for (YjCaJScFeaGeOia , Ge does not have a signifi-
cant effect. But for !Yi.:iCai.7lZiV8i.Fe : i.:tGeo.850i2 and for { VCaojZrFea-
CieOpj the differences are substantial. These differences may be partly
a result of a substantially different effect on the interaction geometry
by the Ge 4+ ion as compared with the Si 4+ ion and partly because some
of the Ge 4+ ions enter octahedral sites in these garnets.
We have also prepared and made measurements on {Yi. 8 Cai. 2 |-
[Zro. 6 Fei.4](Sio.6Fe2.4)Oi2 and {Yi.sCai/ilZro.eFes.sOeo.eO^ (Tables V and
VI) for comparison with |Y 3 )[Mgo.6Fei. 4 ](Sio.6Fe2.4)Oi 2 (Fig. 11).
608 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
Although the differences are small, they could be real. The Mg-substi-
tuted garnet has the highest moment and the Zr-Ge substituted one
the lowest. Again in the latter case, it is possible that some Ge ions
substitute in octahedral sites.
For the most part, however, in the region in which magnetic satura-
tion is attained, differences in behavior for different nonmagnetic ions
are either insignificant or small, as can be seen from an examination of
Tables IV, V and VI and from later discussion. There is one garnet
listed in Table V which behaves anomalously, as will be seen more
clearly later; it is jYo.8Ca 2 .2HZi'o.6Fei.4](Fei. 4 Sii.6)Oi 2 . Although its
moment appears to be right, its Curie temperature appears to be too
low. This garnet, however, was very difficult to make. Although its
lattice constant indicates that the composition is as given, the back-
reflection lines in the powder photograph were not sharp.
It appears then that wc must conclude that, especially in the regions
of substitution in which intrasublattice interactions are dominant,
there is a substantial effect on the magnetic structure of the types of
ions substituted. Once it is realized that this occurs, it is not too diffi-
cult to find reasons that it should.
It has been shown that the geometry of different garnets may differ
substantially. For example in a grossularite ( {Ca 3 }[Al 2 ]( Si :{ )Oi 2 ),' the
oxygen octahedron is much more nearly regular than in yttrium iron
garnet. 32 Also, the oxygen tetrahedron about the Si 4+ ion is more regular
than that about the Fe 3+ ion in yttrium iron garnet. However the
oxygen dodecahedron about the Ca" + ion is more irregular than that
about the Y 3+ ion in yttrium iron garnet. The Si-O-Al angle in the grossu-
larite is 136°, while the Fe(a)-0-Fe(d) angle in yttrium iron garnet is
127°.
Because ions of different valence and size produce different effects
on the geometry (a manifestation of differences in chemical bonding)
or crystal structure, it may be speculated that they will also produce
different effects on the magnetic structure, especially when weak inter-
actions are important (see also Kefs. 21, 24 and 10-13).
In the earlier discussion of the | Y:,)[Mg J Fe 2 _ J ](Fe 3 _ J Si I )Oi 2 system,
it was pointed out that the substitution of Si 4+ ions in the tetrahedral
sites, had, beyond x = 0.70, the tendency to weaken the d-d interactions.
However, it is now seen that the Mg 2+ ion appears also to disrupt the
magnetic structure less than does Sc 3+ or Zr 4+ substitution. Unfortu-
nately, it is again not possible to determine experimentally the separate
effect of the Mg 2+ ion. Nevertheless, if our assumption requiring the
moments in one sublattice to remain parallel is valid, then our conclu-
BEHAVIOR OF SUBSTITUTED YIG
009
sions appear thus far to he. plausihle. In Fig. 22 we have plotted points
for the effective moments of the tetrahedral Fe 3+ ions for x = 0.85 and
1.00 in the garnets { Y; ! _ 2j Ca 2j )[Zr,Fe2-. r ](Fe 3 - I Si,)0 1 2 and (Ya^Ca*}-
[Sc J .Fe»_ J ](Fe S -xSi x )Oi2 . It is seen that these are higher than for the
analogous garnets ( V3- J Ca J }[Zr J Fe2-x](Fe3)0 12 and | Y :I | [ScxFe*-,]-
(Fea)Oi2 respectively.
If there were no effect of particular nonmagnetic ions substituted for
the Fe" + ions, it would he possible to plot a series of curves of 0°K
moment vs /, = ij/(.v + //), where .r,ij equals the number of nonmag-
netic ions in the octahedral, tetrahedral sites respectively. Thus it
would have been possible with limited data to predict the moments for
all nonmagnetic ion substituted yttrium iron garnets. Within the range
that the a-d interactions are everywhere dominant, this is still possible
for the garnets discussed here. We have seen that even when x + V
is large, if y is substantially larger than .r, the a-d interactions may still
be dominant and therefore such curves would still be valuable.
Some curves of this type are plotted in Fig. 27. Included arc curves
-2
^^Os-
a
1
s
x+y =
'o.25
0.50
060
0.70
o.ao
1.00
2.50
1.20
2.20
1.50
1.75
2.00
0.8
r t
Fig. 27 — Spontaneous magnetizations, n B (0,0) of substituted yttrium iron
garnets vs/ ( , the fraction of nonmagnetic ions in the tetrahedral sites, [x = num-
ber of nonmagnetic ions in octahedral sites; ;(/ = number of nonmagnetic ions in
tetrahedral sites;/, = y/(x + //).] Shown also is the curve for the Y 3 Fe5_xAbOij
system.
610
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
which have regions in which the intrasublattice interactions are domi-
nant. Points in the region /, ^ 0.5 are mostly from the system |Y 3+1 _„-
Ca v _ I }[Mg I Fe 2 _x](Fe3- v Si 1/ )0 12 . In Fig. 28, Curie temperatures vs/ t are
shown for some values of x + y. The curves should be considered
rather rough, because not many points have been obtained.
Fig. 27 shows that for x + y = 2.0, there is an algebraic minimum in
the curve at f t tt 0.98. For x + y = 2.20 the algebraic minimum is
more pronounced and occurs at /* ^ 0.93. This makes clearer the
discussion given above regarding the occurrence of garnets in which,
for a given x + y, there is a higher (absolute value) moment when
1(3 - yi) - (2 - Xi)\ < |(3 - y 2 ) - (2 - x 2 )\. Note also that there
are algebraic maxima in the curves for values of x + y > 0.70. The
value of x + y at which the maximum or the minimum first occurs
appears to be at the point at which the intrasublattice interactions
become dominant in the exclusively octahedral and tetrahedral ion
substituted garnets respectively (see above). The crossover point for
the Ge-substituted system should then be at the point of the algebraic
minimum for the Si-substituted system. Examination of Fig. 4 shows
that extension of the curve for the former system does intersect that
of the latter system at about the predicted point.
The arguments regarding the effects of particular ions may be made
still clearer. Referring again to Table VIII, we see that if one wished to
Fig. 28 — Curie temperatures vs ft for various substituted yttrium iron gar-
nets. (The lines connecting the points are, in this case, somewhat speculative.)
BEHAVIOR OF SUBSTITUTED YIG
611
assume that the lower moments for Sc + and Zr 4+ substitution when
.c = y = 1.0 (that is, with one Si 4+ in tetrahedral sites) resulted from
some Sc ,t+ or Zr 4+ ions entering tetrahedral sites, f t for the former
would be 0..56 and for the latter 0.00 (Fig. 27). But then in Fig. 28 we
see that the Curie temperatures should be in reverse order from those
observed. Furthermore, magnetic saturation should also be more, rather
than less, easily attainable than for the analogous Mg 2+ ion substituted
garnet. The garnet [Y£Sa}[Mg«.iFei.i](Fei.iSi].i)OM (f, = 0.75) satu-
rates at %9.0 koe at 1.4°K (see Table V).
Fig. 28 also appears to corroborate the idea that the intrasublattice
interactions are effective over the whole temperature range, since for a
given value of x + y, the maximum value of T c is almost surely attained
when the effective moments are at a maximum. It should be kept in
mind, however, that Figs. 27 and 28 are based mainly on data from
garnets which are magnetically saturated at 1.4°K and the data from
the system | Y 3+J - / ,( , a i/ _ J |[.\Ig J .Fe L ._ J .](Fe 3 _ y Si„)Oi 2 . The data from the
system | Y :i _„Ca„) ISc,Fe2_.,.] ( Fe.i_ tt Si w )Oi 2 in the region where saturation
is not attained must be treated separately, as must the data from such
a system as | Y 3 _ J _ // Ca. r . H/ l[Zr r Feo_,]( Fes-ySi^X)^ . This results, as shown
above, from the effect of the individual nonmagnetic ions on the mag-
netic structure.
Knowing that the (lilleo theory does not account for the 0°K mo-
ments of the substituted garnets and also that the x-ray method is not
apt to give very narrow limits for the ionic distribution in the system
YnFes-jAljt )| 2 , it was felt that it might be determined from such data
as plotted in Fig. 27. If the particular ion effect is neglected, one may
draw a curve (see Fig. 27) intersecting those for particular 39 x + y at
values of n B found in the ^'jFes-jAUO^ system and thereby find f t
for each .»• + y in this system, as plotted in Fig. 29.
The results obtained appear to be reasonable. It will be noted first
0.6
{YajFe^A^O,;,
^"H
1 — ^__
2 3
Fig. 20— /i vs x for the system Y3Fe6-»Al*Ois us derived from Fig. 27.
612 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
that the curve extends naturally from 39 x + y=2.5tox + y = 5.0,
in which// must be 0.60. Secondly, for x < 2.00, (a: as in l^Fes-xAlzOia)
magnetic saturation is obtained at low fields at 1.4°K. Furthermore,
two specimens in the system j Y 3+ x-«Ca„-a}[Mg s Fe»_«](Fe8_ s Sii,)Ois ,
namely those for x = 0.175, y = 0.825 and x = 0.75, y = 1.75 and a
third {Yi.6oCai.Boi[Zr .85l r ei.6B](Fei.8BSii.i6)Oi2 give very good checks
on the moments found in the YaFes-xAlxO^ system (see Tables V and
VII). The Curie temperatures for the three specimens are plotted vs
X + y in Fig. 18 together with those found for the specimens in the
Y3Fe5_(x +I/ )Al (I+I/ )Oi2 system. The agreement in the region x + y ^ 1.50
is good but deteriorates in the region x + y > 1.50. This may again be
an indication of the "particular ion effect."
Now consider a set of substituted garnets which have the same
Curie temperature and which saturate magnetically at low fields. It is
uncertain whether at a given temperature below T c the values of the
intrinsic spontaneous moments per octahedral Fe 3+ ion, M , will all
be the same, and similarly whether those of the tetrahedral Fe 3+ ions,
M t , will be the same. It is unlikely, however, that they will differ
greatly, and we shall assume that they are the same.
We take the three garnet specimens with measured extrapolated or
interpolated Curie temperatures 367-375°K:
(1) jY l .6oCa 1 . 5 oHZro.35Fe 1 . 65 ](Fei.86Si 1 . ]5 )0 I2 (T c = 370°K)
(2) {Y 1 .BoCa 1 .5o}[Fe 2 ](Fe 1 . 5 oSi 1 .5o)0 12 (T c = 367°K)
(3) {YaHMgo^Fei.ssKFeo.ssSio^JO^ (T c = 375°K).
(For all these, the values calculated on the basis of the Gilleo model
differ by ^11°K.) The observed spontaneous moments at 0, 100, 200,
and 300°K are respectively as follows:
(1) 0.88, 0.79, 0.59, 0.38 M »
(2) -2.36, -2.15, -1.65, -1.08/z B
(3) 4.46, 4.00, 3.04, 2.00 n„ (by interpolation; see Fig. 30).
In specimen ( 1 ) the canting must take place in the d sites, the sine of
the angle being 0.99 [i.e., (5(1.65) + 0.88}/ (1.85)5]. In (2) the cant-
ing occurs in the octahedral sites, the sine of the angle being .99.
Designating the octahedral and tetrahedral moments M„ and M t re-
spectively, we have from (1) and (2) at 100°K:
1.85(0.99)il/ t - IMMo = 0.79 vlb
1.503/, - 2(0.99)M o = -2.15mb
BEHAVIOR OF SUBSTITUTED YIG
613
W[Mg x Fe 2 _ a .](Fe,_ a .SL se )o ia
k°AA
\
m
\\\\|
1.0
X
?.o
Fig. 30 — Spontaneous magnetizations, n B (H a = 0), vs x for given temperatures
in the {Ys)[Mg,Fej_](Fei_Si x )0,. system.
for which
and
M, = 4.44 M/(
M„ = 4.45
Mu
For (3), we should have
2.38(0.96)Jlf, - 1.38M = 4.00 y. B ,
the canting angles being obtained from the effective moments given in
Fig. 22. Putting the moments obtained from (1) and (2) into the ex-
pression for (3), we obtain 4.00 p B .
To obtain the other values for (3) we substitute the 200 and 300°K
moments in turn for the 100°K ones. At 200 °K, we obtain from (1) and
(2) M t = 3.36, M = 3.38 m« , and the net moment for (3) calculated
from these Fe ion moments is 3.01 n H , to be compared with 3.04
H B observed. At 300°K, (1) and (2) yield i\I , = 2.14 y. B , M = 2.17
u fl ; the net moment calculated for (3) from these is 1.80 /x« , to be
compared with 2.00 y. B observed. The agreement of calculated with
observed values is generally good.
614 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
Now we try the same procedure with the Gilleo model. The three
equations would be
(1) 1.85(0.97)M< - 1.65(0.96)M = n B m {T)
(2) 1.50JI/, - 2.00(0.89)M = n B m (T)
(3) 2.38(0.91)M, - 1.38(0.99)M o = n B m (T).
If we solve (2) and (3) of the Gilleo model for T = 100°K, we ob-
tain M t = 5.57 fi B and il/„ = 5.90 p B , clearly impossible values, and
there is therefore no point in checking these equations further.
It therefore appears that the intrasublattice interactions in these
garnets may be important over the whole temperature range to or near
T c and that the Gilleo model is inapplicable in this range. However,
the agreement of observed Curie temperatures with those predicted by
the Gilleo theory is so good as to indicate either that the Gilleo theory
is applicable very near the Curie temperature or that agreement is
somehow fortuitous. In any case the Gilleo formula for Curie tempera-
ture is useful for the garnets of the systems discussed here.
When the canting model favored in this paper is used to calculate
the intrinsic moments of the Fe 3+ ions in the two different sites, the
values obtained are only slightly different; in fact, the difference is so
slight as to appear insignificant. The work of Bertaut et al., 40 Prince
and Kuzminov et al., 42 indicates that in yttrium iron garnet itself, the
moments at temperatures above 110°K of the crystallographically
different Fe 3+ ions are substantially different. This is not corroborated,
at least by the results on the substituted garnets.
There is some question as to how the determinations of the spon-
taneous magnetizations should be made when saturation is not attained
at fields up to 14.24 koe. This "unsaturation" occurs noticeably after
the intrasublattice interactions become dominant, an indication that
the tendency not to saturate is associated with the canting. It is
probable that when a specimen appears not to be saturated it is, in a
sense, "oversaturated"; that is, the applied field disrupts the true zero-
field structure by causing some alignment of the canted moments. If
such were the case, it would appear that extrapolation to zero field
would yield the more nearly correct results. This was especially well
demonstrated by the results on the {Ys}[Mg,Fe 8 -J(Fej_ x Si*)Oi2 system.
It is possible, however, that increased anisotropy also plays a role in
preventing saturation. Measurements on single crystals, not now avail-
able, should aid in clarifying this situation.
In Gilleo's theory, an Fe 3+ ion in one coordination not linked to at
BEHAVIOR OF SUBSTITUTED YIG 615
least two Fe ions in the other coordination does not participate in
the ferrimagnetism, at least at temperatures above 20 °K. Gilleo points
out that the ions thus excluded should behave nearly as free ions at
these temperatures, i.e., between 20 °K and T c . We do not find this
to be the case. For example, in the j Y»-^Ca«}[Fed(Fet-J3i«)Oii system,
for substitutions which have the a-d interactions dominant, that is,
for x t < 1.92 and x„ < 0.70, the specimens are saturated or very nearly
so at nominal fields. Beyond x t = 1.92 or x = 0.70 saturation is not
attained even at 1.4°K. But generally we observe that n B (H„,T) —
n B (0,T) for fixed//,, < 14.24 koe is essentially constant to temperatures
somewhat below the Curie temperature. For example, in the case of
{YCa 2 )[Fe 2 ](FeSi 2 )0 12 with T c = 20G°K, n B (H a ,T) - n B (0,T) is
approximately equal to 0.2 \x B at H a = 14 koe to T « 220°K. In the
case of {Yo. B Ca,.5}[Fe 2 ](Feo. 5 Si...5)0 12 with T c = 86°K, n B (H a ,T) -
n B (0,T) is approximately equal to 0.f> n„ at //„ = 14 koe to T « 80°K.
4.1 Application to Ferrospineh
In the present article, it has been shown that the substitution of any
nonmagnetic ion for an Fe' + ion in the garnets tends to weaken the
average a-d interaction. In a previous paper, 14 it was shown that divalent
paramagnetic ions and Cr ' ions also tend to weaken the average a-d
interaction when substituted for the Fe 3+ ions. The weakening of these
interactions also results in an apparent reduction of the effective moment
of the magnetic ions in at least one of the sublattices. We have put
forward the idea that this reduction may be the result of random cant-
ing of these moments resulting from the intrasublattice antiferromag-
netic interactions.
The ideas discussed in this paper should be applicable to the ferri-
magnetic spinels. In a spinel, there is one cation in a tetrahedral site
and there are two cations in octahedral sites per formula unit AB0O4 .
The antiferromagnetic interactions between magnetic ions on the two
different sites would be expected to be the strongest present in the
crystal; the antiferromagnetic interactions within the octahedral sub-
lattice would be expected to be stronger than the antiferromagnetic
interactions within the tetrahedral sublattice.
In the system ( Yj_ x Ca x }[Fe 2 ](Fe 3 -xSi,)Oi2 , there is very little effect
on the effective moment of the Fe 3+ ions in octahedral sublattice of
substitution to x = 1 .0, and only small effect even to .r = 1 .50. Thus one
would predict that substitution in the octahedral sublattice of a ferro-
spinel would give similar behavior. On the other hand, substitution for
616 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
a-site Fe s+ ions in the garnets has almost an immediately obvious effect
on the effective moments of the Fe 3+ ions in the d sites. Similarly,
substitution in the tetrahedral sites of the ferrospinel might be expected
to have a substantially larger effect than an analogous (twofold) sub-
stitution in the octahedral sites.
Lithium ferrite, (Fe)[Li . B Fe 1 . 5 ]O4 , accordingly has the highest Curie
temperature, 083>°K, a among the ferrospinels. Any substitution — i.e.,
by paramagnetic or nonmagnetic ions — for trivalent Fe" + ions in this
spinel reduces the Curie temperature. 43 Now the spinel nickel ferrite is
inverse, 44 i.e., the formula may be written (Fe)[NiFe]0 4 . In the garnet
(Y 3 }[Ni 2 ](FeGe2)Oi2 , the Ni 2+ -0 2_ -Fe :,+ interaction is about ^ as strong
as the Fe 3+ -0 2_ -Fe' H interaction. 14 In ( Fe)[Li .5Fei. 5 ]O 4 , each tetra-
hedral Fe 3+ ion is linked through oxygen ions, on the average, to three
Li 3+ and nine Fe 3+ ions in the octahedral sublattice; in (Fe)[NiFe]0 4
each tetrahedral Fe 3+ ion is linked, through oxygen ions, on the average
to six Ni 2+ and six Fe 8+ octahedral ions. In both cases, octahedral ions
are linked only to Fe 3+ ions in the tetrahedral sublattice. The average
interaction strength in (Fe)[Lio.5Fei. 5 ]0 4 is then f^9/8 of that in
(Fe)lNiFe]0 4 . If there were at least an approximately linear relation-
ship between Curie temperature and interaction strength, 45 the Curie
temperature of (Fc)[NiFe]0 4 should be ^ 850°K. This value compares
favorably with that observed, 853°K.
Several investigators have sought an explanation for the low 0°K
moment observed for manganese ferrite. As far as we know, there has
been no direct evidence of other than divalent manganese and trivalent
iron in a carefully prepared ferrite of composition MnFe 2 ()4 • Now man-
ganese ferrite has a low Curie temperature, 603°K, as compared with
nickel ferrite. Our work on the garnets would indicate that the strength
of the Mn 2+ -0 2 -Fe 3+ interaction should not differ substantially from
that of the Ni 2+ -0 2 ~-Fe 3+ interaction. Thus, the low Curie temperature
must be associated with the evidence that MnFe 2 4 is actually an almost
normal spinel, that is, the distribution of ions is given by
(Mn .8iFeo.i9)[Fei.8iMno.i 9 ]0 4 . 4fi ' 47
But this is analogous to the substitution in the a sites in yttrium iron
garnet. Now an Fe 8+ ion in an octahedral site in the ferrite is linked to
mostly Mn 2+ ions in tetrahedral sites; thus the average a-d interaction
is substantially weaker in this ferrite than in lithium ferrite, and ac-
cordingly the Curie temperature is substantially lower.
We have shown 14 also that even substitution of 0.4 Mn 2 in the a
sites of yttrium iron garnet causes canting of the r/-site ion moments.
BEHAVIOR OF SUBSTITUTED YIG 617
We propose that the behavior of manganese ferrite is similar to that of
the divalent magnetic ion substituted garnets; that is, that the substitu-
tion of any ions for Fe' ions causes a weakening of the a-d interactions,
whereupon the competing intrasublattice interaction manifests itself.
For MnFe 2 04 the usually observed value of the spontaneous magnetiza-
tion at 4.2°K is 4.6 n B . Hastings and Corliss 46 have measured three
specimens which give this value and very nearly the same ionic dis-
tribution. However, they could not resolve the problem of the low
moment.
It is possible that if the specimens were not stoichiometric a low value
could be obtained. However, if it is accepted that 4.6 Ms is the correct
value of spontaneous magnetization at 4.2°K, then we have, analogously
to the garnets, that the canting may occur among the Fe 3+ and Mn" +
ion moments on the (/-sites. The effective moment (i.e., the component
antiparallel to the a sublattice Fe' 1 ' ion moments) of a r/-site ion would
then be 4.8 n B ■ In the garnet |Y 3 ) [Mn .4Fei.6](Fe 2 . 6 Siu.4)Oi2 , the effec-
tive r/-site Fe + ion moment is 4AM). Comparisons (see Fig. 22) with the
effects of substitution of nonmagnetic ions in the garnets lead intuitively
to the conclusion that the proposed amount of canting of the octahe-
dral cation moments in manganese ferrite is plausible.
In discussing this conclusion with Hastings and Corliss, they have
informed us that in the course of their investigation of MnFe204 they
considered the moments proposed by us but concluded that the value
of 4.6 hi, for the average moment per ion in each sublattice gave a better
fit with the observed data. This conclusion has not been changed after
recent further consideration; however, the authors inform us that the
model proposed by us cannot be ruled out by the existing data.
4.2 Neutron Diffraction Studies
We should mention what our ideas mean as far as neutron diffraction
studies are concerned. First, consider a crystalline substance which is a
solid solution. Coherent x-ray dill' taction effects average over the crystal;
that is, they do not tell us about local or short-range structure. For
example, if two chemically different kinds of atoms may be thought to
occupy highly specialized space group positions (i.e., with no allowable
degrees of freedom), these are seen by the coherent x-ray "reflections"
as having a weighted average atomic form factor of the two different
atoms. Further, it could happen that these atoms, in the short range,
may not lie exactly on the space group sites, but over the crystal space;
that is, in the long range, appear to lie on these sites. In such a case the
618 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
average thermal parameter may look too high, because the displacements
of the atoms from the exact sites will appear from the coherent x-ray
diffraction effects to be vibrations. Only the incoherent scattering will
contain the information sought, but this may be too complicated to
interpret.
Similarly, coherent neutron diffraction reflections may not give us a
direct insight into the short-range magnetic disorder of the substituted
garnets. They will give us only the average effective moment per ion
of the particular sublattice. Incoherent neutron scattering might, how-
ever, be more elucidating.
4.3 Garnets Containing Pentavalent Vanadium and Antimony
Recently we have discovered new garnets containing pentavalent
vanadium and antimony ions. In the case of V 5+ ion substitution Smolen-
skii et al. 9 had reported on the system x ( YCa 2 ) Fe 4 VOi 2 - ( 1 — x)
Y 3 Fe 2 Fe 3 0i 2 but could not obtain a single-phase specimen with
x = 1.0. We found that we could obtain a single-phase garnet with
formula fCa 3 }[Fe 2 ](Fe,. 5 Vi.5)Oi 2 and that the complete solid solution
range in the system (Y 8 _sxCa 2l }[Fe a ](Fe 3 _ a! V«)Oi 2 exists. 1112 The end
member, i.e., with x - 1.5, has a 0°K moment not significantly different
from that of the Si 4+ ion substituted garnet ( Yi . B Cai .5} [Fe 2 ] ( Fei . 5 Sii . B ) 12 ,
but its Curie temperature, 493°K, is 126°K higher than that of the Si 4+
ion substituted garnet. In the range of x studied, the Curie temperatures
of the system { Y 3 _ 2j Ca 2 x)[Fe 2 ](Fe 3 _*V x )Oi2 are all higher than those for
{Y 3 _ I Ca x }[Fe 2 ](Fe 3 _ J Six)Oi 2 for the same x. In fact, the Curie tempera-
ture, 563°K, of { Y 2 . 2 Cao.8}[Fe 2 ](Fe 2 . 6 Vo.4)Oi 2 is even higher than that of
YIG itself. This behavior could not have been predicted from the re-
sults on the systems discussed in detail in this paper.
It was also found 12 that garnets in the yttrium-free jBi 3 _ 2j Ca 2l }[Fe 2 ]-
(Fe 3 _ x V*)Oi2 system could be prepared, the probable range of x being
1.5 > x > 0.8. In particular the magnetic behavior of |Bi . B Ca 2 . B }[Fe 2 ]-
(Fe,.7 5 Vi. 2B )Oi 2 is essentially the same as that of the yttrium analog,
despite the fact that Bi 3+ for Y 3+ ion substitution in YIG, i.e., in the
system {Y 3 _. f Bi. r JFe 2 FesOi 2 , resulted in increased Curie temperature. 13
Pentavalent antimony may be put into garnets, 1 " as in the system
{Y 3 _ 2 xCa 2j j[Fe 2 _,Sb,](Fe 3 )0 12 ; garnets exist over the whole range
^ x ^ 1 .5. To x K. 0.0 this system behaves similarly to the Sc 3+ and
Zr 4+ ion substituted systems at 0°K, but with some differences at higher
temperatures. In the high substitution region, 0°K moments of the
system are substantially lower than those of the Sc 3+ and Zr ion
BEHAVIOR OF .SUBSTITUTED YIG 619
substituted systems. The turn down (see Fig. 4) of 0°K moment occurs
sooner for the Sb ion substituted system than for the other two.
The end-member [Ca 3 }[Sbi.5Feo.5](Fe3)Oi2 forms a complete solid
solution range with |Ca 3 )[Fe 2 ]( Fei. 5 Vi. 5 )Oi2 ; the system may be written
(Ca3}[Sb J Fe 2 _i](Fei.5+xV l .5_x)Oj2 . The behavior of this system 10 could,
in part, have been predicted from the results given in this paper. How-
ever, for x = 0.75, for example, the specimen does not saturate at
moderate fields and its moment at 4.2°K is 2.5 n„ . This may be com-
pared with the 0°K moment, 4.35 m» , of { Y ;) J [Mg,i. 7 5Fei. 2 5](Fe 2 2 6Si .7&)Oi 2 ,
which is magnetically saturated at moderate fields.
Further details regarding those garnets and others involving Sb 5+ and
V 5+ ion substitution will be found in Refs. 10-12. In the cases of Sb 5 *
and V 5+ ions, their effects on the magnetic interactions occur even when
substitution is not large. Therefore, even in these regions, all the results
could not have been predicted from those of the present paper. Never-
theless, the ideas given in the present paper may still account for the
behavior; we have pointed out earlier that systems which show large
differences must be treated separately.
IV. A C KN O W LEDG M E N TS
We wish to thank Y. Yafet for discussions of the theory of which he
is coauthor, E. A. Nesbitt for the Curie temperature measurements as
indicated in Table I, and A. J. Williams for technical assistance. Fig. 2'S
was drawn by II. J. Seubert and Fig. 24 is reproduced from Rcf. 48.
Note Added in Proof
To ensure that the reader who so wishes may be able to duplicate our
results, we have decided to list the preparation conditions of all speci-
mens, rather than only those of Table IV. In Table IX the firing tem-
perature is given, followed by the number of hours at that temperature.
Each comma represents a regrinding and recompacting of the specimen.
All firings were carried out in air except as indicated. In garnets con-
taining Ca 2+ and Mg 2+ ions, starling materials were carbonates of these;
in such cases a calcining was carried out. Usually, this consisted of vary-
ing the temperature in the initial firing from 500 to 000°C over a period
of 1-2 hours.
It should be emphasized that the magnetic and crystallographic meas-
urements were always made on the specimens quenched rapidly in air
from the last firing temperature.
Table IX — Preparation Data
Firing conditions, °C (hr.)
|Y3-xCa,)[Fe 2 ](Fe 3 -,Si,)0 1 2
0.00
1405(1(5)
0.40
1435(15)
0.75
1160(1), 1375(23)
1.00
1410(16), 1435(10), 1400(18), 1450(66)
1.01
1250(2), 1380(16), 1330(18), (75)
1.02
1250(1), 1285(17), 1275(20), 1415(7)
1.50
1280(16), 1300(19), (68), 1350(40)
1.77
1235(1), 1275(4), 1295(2), 1300(40), (?)»
1.88
1225(1), 1265(5), 1280(18), 1300(16)
2.00
1200(2), 1270(2), 1300(21), (18), (19)
2.25
1225(1), 1205(2), (2), 1285(6)
2.50
1225(1), 1260(2), 1265(48), 1260(1), 1270(21)
2.75
1225(1), 1200(64), 1220(22), 1240(19), 1245(64)
{Y^ t Ca,|Fe s _,Ge,0, s
0.70
1225(1), 1350(8), 1390(19)
1.00
1340(16), 1320(16), 1300(66), 1435(17), (6)
1.50
1280(16), 1300(19), (68), 1350(40)
1.75
1225(1), 1260(11), 1300(2), 1350(21), 1385(11)
2.00
1225(1), 1250(2), 1280(2), 1330(21), 1385(11)
2.25
1225(1), 1250(2), 1300(2), 1350(2)
2.50
1225(1), 1200(1 ) b , 1280(2) b , 1330(3) b , 1360(2) b , 1400(41)
1420-1370(17)
2.75
1225(11), 1300(2), 1350(3), 1365(2), 1225(7)
[Y s }[Sc*Fea_J(Fei)Oi,
0.60
1300(1), 1350(21), 1395(21)
0.72
1250(1), 1300(2), 1350(21), 1400(2), 1425-1450(4)
0.80
1300(1), 1400(3), 1420(17)
1.00
1250(1), 1325(4), 1400(16), 1440(21)
1.25
1300(1), 1350(21), 1400(41), 1420(21)
1.50
1300(1), 1350(21), 1400(41), 1420(21)
I Ys-«Ca*) [Zr,Fe2_,](Fe»)Ou
0.60
1280(1), 1320(19), 1300(65), 1325(40)
0.72
1300(1), 1350(21), 1350(3), 1380(2), 1425(14), 1400(19)
0.80
1350(1), (5), (5), 1355(22), 1400(16), 1450-1430(18)
1.00
1250(1), 1325(4), 1350(4), 1400(16)
1.25
1300(1), 1350(5), (16)
1.50
1300(1), 1350(3), 1320(161)
1.75
1300(1), 1350(5), (16)
1.95
1300(1), 1350(3), 1320(161)
(Y»_ y+ «Ca„-*}[Mg I Fe*_d(Si I ,Fes_v)Oi2
0.175
0.825
0.30
1.47
0.18
1.57
0.90
1.10
0.50
1.50
0.44
1.76
0.22
1.98
0.75
1.75
1275(1), 1350(2), 1390(2), 1400(21), 1315(18)
13(H)(1), 1350(4), 1375-1400(5), 1180(63), 1275(16), 1360(16)
1205(1), 13(H)(3), 1330(4), 1390-1360(22)
1300(1), 1450-1420(17), 1400(6)
1300(1), 1375(2), 1380(3), 1385(2)
1300(1), 1375(2), 1385(2), 1380(31)
1250(1), 1300(2), 1315(2), 1300(21), (16), 1200(19), 1340-1345(68)
1290(1), 1325(5), 1395(4), 1340(70), 1400(20), 1190(17)
620
Table IX — Preparation' Data — continued
Firing conditions °C (hr.)
{Ys-„Ca,}[Sc,Fc2_,](Si B Fe3-,,)Oia
0.85
0.85
1225Q), 1350(3), 1400(10), 1395(20), 1425(5)
0.30
1.47
1285(1), 1325(4), 1350-1310(21), 1345(29)
0.30
1.52
1275(1), 1300(5), 1340(23), 1320(19), 1350(17)
0.30
1.G0
1250(1), 1300-1330(3), 1340(21), 1360(22)
1.10
0.90
1300(4), 1400(3), (10), 1450(16)
1.00
1.00
1300(4), 1325(2$), 1400(5), 1450(3), 1500(4)
0.90
1.10
1300(1), 1355(3), 1400(20), (16)
[Ya_«_,Ca, +I ,}[Zr,Fe*_x](Si 1 ,Fe I _v)Oi 2
0.76
0.24
1285(4), 1360(2), (2), 1395(3), 1330(10), (42)
0.00
0.60
1275(1), 1300(4), 1310(22), 1340(23), 1365(70)
0.35
1.15
1225(4), 1325(3*), 1360(2), 1250(16), 1300(21)''
0.30
1.20
1250(4), 1350(4), 1375-1400(20), 1400(65), 1315(21), 1300-1275(41)
0.85
0.85
1200(4), 1325(4), 1375(5), 1360(16), 1210(68)''
0.30
1.60
1200(4), 1325(4), 1330(20), 1210(68), '-1330(16), 1350(21)
1.10
0.90
1300(1), 1355(3), 1375(23)
1.00
1.00
1275(4), 1350(2), 1360(24), (24), 1305(21), 1300(16), 1360(20),
1400-1385(66)
0.90
1.10
1200(4), 1325(4), 1375(5), 1360(16), 1210(08) b , 1280(23)
0.60
1.60
1200(1), 1260(4), 1300(4), 1350(4), 1375(4), 1360(16), 1355(16),
1300(70), (118), 1180(63)
1.25
1.25
1250(4), 1325(4), 1350(4), 1355(16), 1375(20), 1270(64), 1350(19)
( Y 3 _„ ^Ca,,..,] MgxFe6-«_»Ge„Oi a
1.00
1.25
1.00
1.25
1250(4)
1330(4)
1300(4), 1395(5), 1450-1460(3), 1500-1525(28), 1340(10)
1400(4), 1410(16), 1400(22)
(Ys-i/CaKJSc-Fes-x-yGevO^
1.00
1.00
1200(4)
1300(44), 1390(21), 1400(22)
{ Y 3 -j-vCa z+ y ) ZrxFes-z-»Ge„0] 2
0.60
0.85
1.00
0.60
0.85
1.00
1275(1)
1200(4)
1250(4)
1300(4), 1310(22), 1340(22), 1365(70), 1385(16)
1300(34), 1330(16), 1340(21), 1315(16), 1340(23), 1375(18)
1325(24), 1375(4), 1425(20), 1450(3)
Y 3 Al J Fe 6 _ I 12
1400(1), 1440(16), 1475(48)
1450(2), 1500(16), 1475(40)
1300(1), 1450(2), 1490(2), (2), 1510(4)
1400(1), 1500(19)
1450(1), 1525(24), 1540(17), 1530(64), 1600-1060(5)
1300-1340(2), 1350-1430(3), 1420(40), 1520(42)
1425(1), 1445-1520(5), 1480(40), 1500(10), 1535(24)
" Unknown because of furnace burn-out.
'■ Fired in 2 .
021
622 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1964
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Solids, 12, Jan., 1960, p. 111.
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Solids, 13, May, 1960, p. 28.
3. Gilleo, M. A., J. Phys. Chem. Solids, 13, May, 1960, p. 33.
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Izvestia, Ser. fiz., 26', 1901, p. 1396.
10. Geller, S., Williams, H. J., Espinosa, G. P., and Sherwood, R. C, J. Appl.
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11. Geller, S., Espinosa, G. P., Williams, H. J., Sherwood, R. C, and Nesbitt,
E. A., Appl. Phys. Letters 3, Aug. 15, 1963, p. 60.
12. Geller, S., Espinosa, G. P., Williams, H. J., Sherwood, R. C, and Nesbitt,
E. A., J. Appl. Phys., Mar., 1964.
13. Geller, S., Williams, H. J., Espinosa, G. P., Sherwood, R. C, and Gilleo,
M. A., Appl. Phys. Letters, 3, July 15, 1963, p. 21.
14. Geller, S., Williams, H. J., Sherwood, R. C, and Espinosa, G. P., J. Phys.
Chem. Solids, 23, 1962, p. 1525; see also J. Appl. Phys. 33, Mar., 1962, p.
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1956, p. 572.
16. Candela, G. A., and Mundy, R. E., Rev. Sci. Instr., 32, 1961, p. 1056.
17. In subsequent discuBBion, these will be considered to be indistinguishable
from the 0°K moments, although they may differ slightly from them.
18. Geller, S., and Miller, C. E., Amer. Min., 44, Nov .-Dec., 1959, p. 1115.
19. Yoder, H. S., and Keith, M. L., Amer. Min., 36, July-Aug., 1951, p. 519.
20. Skinner, B. J., Amer. Min. 41, May- June, 1956, p. 428.
21. Bozorth, R. M., and Geller, S., J. Phys. Chem. Solids, 11, Oct., 1959, p. 263.
22. In a previous paper, 2 it was reported that \ YCa 2 )[Zr 2 ](Fe 3 )0 12 , iYCa 2 )[Zr 2 ]-
(AIo.bFc j. &)(),* and | YCanKZroKGiifl.sFeo.BjO,.. had residual moments at 1.4
K. It now appears (see text which follows) that both |\Ca 2 | [Zr 2 ](Fe.i)Oi 2
and | YCa 2 )lHf .|(Fe 3 )0, 2 , also reported in that paper, could not have been
precisely single-phase garnet specimens and that this was not discernible
at the time of that investigation. With regard to the 0.5 Al and 0.5 Ga
specimens, although t hese should exist as single-phase garnets, it is possible
that these also were not phase pure; the present result on the 0.25 Ga speci-
men is considered to be more reliable.
23. The successful preparation of this garnet is a consequence of the fact that
the tetrahedral Ga 3+ -0 2_ distance is expected to be substantially Bhorter
than the tetrahedral Fe 3+ -0 2_ distance. See Geller, S., J. Chem. Phys.
33, 1960, p. 676, and Refs. 14 and 24.
24. Geller, S., J. Appl. Phys. 31, May, 1960, p. 30S.
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26. Neel, L., Ann. Phys., 3, 1948, p. 137.
27. Anderson, P. W., Phys. Rev., 102, May 15, 1956, p. 1008.
28. Until recently, silicon has been known to have only tetrahedral coordination
to oxygens in oxide systems. A rutile type Si0 2 (i.e., with Si having octa-
hedral coordination to oxygens) was shown to occur at very high pressure,
160,000 kg/m 2 , and a temperature of 1200-1400°C. (Stishov, S. M. and Pop-
ova, S. V., Geokhimiya, 1961, p. 837.)
29. Woitowicz, P. J., J. Appl. Phys., 33, June, 1962, p. 1957.
30. Aleonard, R., J. Phys. Chem. Solids, 15, Aug., 1960, p. 167.
31. The term "effective moment" is used rather loosely here to prevent awk-
wardness in the presentation. Throughout the discussion, we shall mean
BEHAVIOR OF SUBSTITUTED YIG 623
by this term the average component of the moment which is antiparallel
to the Fe 3+ ion moments of the sublattice in which there is no canting.
32. Geller, 8., and Gilleo, M. A., J. Phvs. Chem. Solids, 3, 1957, p. 30; 9, 1959,
p. 235.
33. That is, the average d-d (a-d) interaction strength multiplied by the number
of nearest neighbor d(a) cations, 4(8), is greater than six times the average
a-d interaction strength.
34. v. Naray-Szabo,St., Z. Kristallogr., (A), 94, 1930, p. 414.
35. The minus sign, as usual, indicates that the octahedral sublattice contribu-
tion to the spontaneous magnetization is dominant. The (iilleo theory
predicts a moment of —0.65 hh , but a Curie temperature of 242°K for this
garnet.
36. Dauben, C. H., and Templeton, 1). H., Acta Cryst., 8, 1955, p. 841.
37. Geller, S., Miller, C. 10., and Treuting, R. G., Acta Crvst., 13, I960, p. 179.
38. Abrahams, 8. C., and Geller, S., Acta Cryst., 11, 1958, p. 437.
39. In YaFeu-jAlxOio , x is the total substitution of Al distributed over a and </
sites, and therefore is equivalent to x + y of Fig. 27.
40. Bertaut, F., Forrat, F., Herpin, A., and Meriel, P., Compt. Rend. 243, 1956,
p. 898.
41. Prince, E., Acta Cryst., 10, 1957, p. 787.
42. Kuzminov, U. S., Yamzin, I. I., and Belov, N. V., Kristallografiya, 7, 1962,
p. 1946.
43. Gorter, K. W., Philips Res. Rept., 9, August, 1954, p. 403.
44. Hastings, J., and Corliss, L., Rev. Mod. Phys., 25, Jan., 1953, p. 114.
45. Gilleo, M. A., Phys. Rev., 109, Feb. 1, 1958, p. 777 and pertinent references
therein.
46. Hastings, J., and Corliss, L., Phys. Rev., 104, 1956, p. 328.
47. Nozik, Yu. Z., and Yamzin, I. I.', Kristallografiya, 6, 1961, p. 923.
48. Geller, S.. Acta Crvst., 12, 1959, p. 944.
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